Chapter II. Correlation between the laws of formal logic and dialectical logic Dialectics "does not abolish formal logic, but only deprives it of the laws of the absolute meaning ascribed to them by metaphysicians." G. Plekhanov 1. Determine which of the following statements represent

Thinking as an object of study of logic. The role of thinking in cognition

Thinking is the highest in relation to the sensory form of reflection of being, consisting in purposeful generalized cognition of a person, an essential connection and relations of reality

Logic is the science of universally significant forms and means of thought necessary for rational knowledge in any field.

Thinking is a process of indirect reflection of reality. With the help of the senses, one can cognize only that which directly affects or influenced the senses.

Thinking is a process of actively reflecting reality. Activity characterizes the entire process of cognition as a whole, but above all - thinking. Applying generalization, abstraction and other thinking techniques, a person transforms knowledge about the objects of reality.

No matter how great the value of thinking, it is based on data obtained with the help of the senses. With the help of thinking, a person cognizes such phenomena inaccessible to sensory knowledge as the movement of elementary particles, the laws of nature and society, but the source of all our knowledge about reality is ultimately sensations, perceptions, ideas.

So, logic (in the broadest sense of its subject) examines the structure of thinking, reveals the underlying laws. At the same time, abstract thinking, in general, indirectly and actively reflecting reality, is inextricably linked with language. Linguistic expressions are that reality, the structure and method of use of which gives us knowledge not only about the content of thoughts, but also about their forms, about the laws of thinking.

Formal logic: its subject, place, role in the system of scientific knowledge

It is customary to call logic formal, since it arose and developed as a science of the forms of thinking. It is also called traditional or Aristotelian logic. Formal logic studies the objectively formed structure of the thought process, the established connections of concepts and judgments when deriving new knowledge in inferences. It is quite natural that the stable connections of the elements of correct thought acquire the character of laws. The analysis of such connections, along with the description of the structural forms of thinking, is the subject of study of formal logic. Therefore, the subject of logic is:

1. Laws, which are subject to thinking in the process of knowing the objective world.

2. Forms of the thought process - concepts, judgments and inferences.

3. Methods for obtaining new inferential knowledge - similarities, differences in accompanying changes, residues, and others.

4. Ways to prove the truth of the knowledge gained

The task of formal logic is to establish the rules for ensuring the harmony and consistency of true thinking. Not covering all aspects of the cognitive process, formal logic is not a universal method of cognition. The laws of this science remain specific laws of thinking, they do not apply to the entire surrounding reality. A feature of the subject of formal logic is also the analysis of the forms and laws of thinking outside of their emergence and development.

It should be emphasized that logic takes an already established form, considering it as something established, without any history of its own.

Logic as a science of thinking. Subject and object of logic.

1. The word "logic" comes from the Greek logos, which means "thought", "word", "mind", "regularity". In modern language, this word is used, as a rule, in three meanings:

1) to indicate patterns and relationships between events or actions of people in the objective world; in this sense, they often talk about the "logic of facts", "the logic of things", "the logic of events", "the logic of international relations", "the logic of political struggle", etc .;

2) to indicate the rigor, consistency, regularity of the thinking process; at the same time, expressions are used: "logic of thinking", "logic of reasoning", "iron logic of reasoning", "there is no logic in the conclusion", etc.

3) to designate a special science that studies logical forms, operations with them and the laws of thinking.

Object logic as a science is human thinking. Subject logics are logical forms, operations with them and the laws of thinking.

2. The concept of a logical law. Laws and forms of thinking.

Logical law (law of thinking)- a necessary, essential connection of thoughts in the process of reasoning.

Identity law. Any statement is identical with self: A = A

The law of consistency. A statement cannot be both true and false at the same time. If the statement A- true, then its negation not A should be false. Therefore, the logical product of a statement and its negation must be false: A & A = 0

The law of the excluded third. The statement can be either true or false, there is no third way. This means that the result of the logical addition of the statement and its negation always takes on the value true: A v A = 1

The Law of a Sufficient Basis- the law of logic, which is formulated as follows: in order to be considered completely reliable, any position must be proven, that is, sufficient grounds must be known by virtue of which it is considered true.

There are three main forms of thinking: concept, judgment and inference.

A concept is a form of thinking that reflects the general and, moreover, essential properties of objects and phenomena.

Judgment is a form of thinking that contains an affirmation or denial of any position regarding objects, phenomena or their properties.

Inference - such a form of thinking, in the process of which a person, comparing and analyzing various judgments, derives a new judgment from them.

Formation of the science of logic, stages of its development.

Stage 1 - Aristotle. He tried to find an answer to the question: "How do we reason." He analyzed human thinking, its forms - concepts, judgments, inferences. This is how formal logic arose - the science of laws and forms of thinking.	ARISTOTLE (lat. Aristotle)(384-322 BC), ancient Greek scientist, philosopher
Stage 2 - the emergence of mathematical or symbolic logic. Its foundations were laid by the German scientist Gottfried Wilhelm Leibniz, who attempted to replace simple reasoning with actions with signs.	Gottfried Wilhelm Leibniz (1646-1716) German philosopher, mathematician, physicist, linguist.
Stage 3 - the Englishman George Boole finally developed this idea, he was the founder of mathematical logic. In his works, logic acquired its own alphabet, spelling and grammar. The initial section of mathematical logic was called the algebra of logic or Boolean algebra.	George Boole (1815-1864). English mathematician and logician.
George von Neumann laid the foundation for the work of a computer with a mathematical apparatus that uses the laws of mathematical logic.

An example of expanding the scope of a concept with a simultaneous decrease in content

MSU → State University → University → University → Educational (educational) institution → Educational institution → Institution → Organization → Subject of public law → Subject of law

The law is applicable only when the volume of one concept enters the volume of another, for example: "animal" - "dog". The law does not work for mismatched concepts, for example: "book" - "doll".

A decrease in the volume of a concept with the addition of new features (that is, an expansion of the content) does not always occur, but only when a feature is inherent in part of the volume of the original concept.

Types of concepts.

Concepts are usually divided into the following types: 1) single and general, 2) collective and non-collective, 3) concrete and abstract, 4) positive and negative, 5) non-relative and correlative.

1. Concepts are divided into singular and general, depending on whether they are thought of as one element or many elements. A concept in which one element is thought of is called a single one (for example, "Moscow", "L.N. Tolstoy", "Russian Federation"). The concept in which many elements are thought of is called general (for example, "capital", "writer", "federation").

The general concept referring to an indefinite number of elements is called non-registering. So, in the concepts of "person", "investigator", "decree", the set of elements conceivable in them cannot be taken into account: all people, investigators, decrees of the past, present and future are thought in them. Non-registering concepts have an infinite scope.

2. Concepts are divided into collective and non-collective.

The concepts in which the signs of a certain set of elements that make up a single whole are thought of are called collective. For example, "collective", "regiment", "constellation". These concepts reflect many elements (team members, soldiers and regiment commanders, stars), but this set is thought of as a single whole. The content of a collective concept cannot be attributed to each individual element included in its scope, it refers to the entire set of elements. For example, the essential characteristics of a team (a group of people united by a common work, common interests) are not applicable to each individual member of the team.

The concept in which the features related to each of its elements are thought is called non-collective. Such are, for example, the concepts "star", "regiment commander", "state".

3. Concepts are divided into concrete and abstract, depending on what they reflect: an object (class of objects) or its attribute (relationship between objects).

A concept in which an object or a set of objects is thought of as something independently existing is called concrete; the concept in which the attribute of an object or the relationship between objects is thought is called abstract. Thus, the concepts "book", "witness", "state" are specific; the concepts of "whiteness", "courage", "responsibility" are abstract.

4. Concepts are divided into positive and negative, depending on whether their content consists of properties inherent in an object, or properties that are absent from it.

5. Concepts are divided into non-relational and correlative, depending on whether they think about objects that exist separately or in relation to other objects.

Concepts that reflect objects that exist separately and are thought outside of their relationship to other objects are called irrelevant. These are the concepts of "student", "state", "crime scene", etc.

To determine what kind of concept a concept belongs to is to give it a logical characterization. So, giving a logical characterization of the concept of "Russian Federation", it is necessary to indicate that this concept is a single, collective, concrete, positive, non-relational. When characterizing the concept of "insanity", it should be indicated that it is general (non-registering), non-collective, abstract, negative, and irrelevant.

6. Relationships between concepts. +++++++++++

Comparable concepts. In terms of content, there can be two main types of relations between concepts - comparability and incomparability. Moreover, the concepts themselves are respectively called comparable and incomparable.

Comparable concepts are divided into compatible and incompatible.

Compatibility relationships can be of three types. This includes equivalence, crossing and subordination.

Equivalence. The relation of equivalence is otherwise called the identity of concepts. It arises between concepts containing the same object. The volumes of these concepts coincide completely with different content. In these concepts, either one object is thought of, or a class of objects containing more than one element. To put it more simply, in relation to equivalence, there are concepts in which one and the same object is thought. As an example illustrating the relationship of equivalence, we can cite the concepts of "equilateral rectangle" and "square".

Intersection (crossing). Intersection concepts are those whose volumes overlap partially. The volume of one, therefore, is partly included in the volume of the other, and vice versa. The content of such concepts will be different. The intersection relation is schematically reflected in the form of two partially superposed circles (Fig. 2). The intersection on the diagram is shaded for convenience. An example is the concept of "peasant" and "tractor driver"; "Mathematician" and "tutor".

Subordination (subordination). The relationship of subordination is characterized by the fact that the volume of one concept is completely included in the volume of another, but does not exhaust it, but is only a part.

Incompatibility relations are usually divided into three types, among which they are distinguished subordination, opposition and contradiction.

Submission. A subordination relationship arises when several concepts are considered that exclude each other, but at the same time have subordination to another, common to them, wider (generic) concept.

Opposite (contrast). The concepts in relation to the opposite can be called such species of the same genus, the contents of each of which reflect certain characteristics, not only mutually exclusive, but also replacing each other.

Contradiction (contradictory). The relationship of contradiction arises between two concepts, one of which contains certain features, and the other denies (excludes) these features, without replacing them with others.

Comparable- these are concepts that, in one way or another, have common essential features in their content (by which they are compared - hence the name of their relationship). For example, the concepts of "law" and "morality" contain a common feature - "social phenomenon".

Incomparable concepts. Incomparable- concepts that do not have any essential in one way or another common features: for example, "right" and "universal gravitation", "right" and "diagonal", "right" and "love".

True, such a division is, to a certain extent, conditional, relative, for the degree of incomparability can also be different. For example, what is common between such seemingly different concepts as "spaceship" and "fountain pen", except for some, purely external similarity in the form of the structure? And yet both are the creations of human genius. What is common between the concepts of "spy" and "letter b"? As if nothing. But here is what unexpected association they evoked in A. Pushkin: “Spies are like the letter b. They are needed in some cases only, but even here you can get by without them, but they are used to sticking around everywhere. " This means that the common feature is "sometimes necessary."

There are incomparable concepts in any science. They also exist in legal science and practice: "alibi" and "pension fund", "guilt" and "version", "legal adviser" and "independence of a judge", etc., etc. Incomparability characterizes even seemingly , which are similar in content to the concepts: "enterprise" and "enterprise administration", "labor dispute" - "consideration of a labor dispute" and "a body for considering a labor dispute", "collective agreement" and "collective bargaining on a collective agreement." It is important to take this circumstance into account in the process of operating with such concepts, so that, contrary to desire, not to fall into a comic position.

Classification of judgments.

The predicate judgments, will be the bearer of novelty, may have a very different character. From this point of view, in all the variety of judgments, there are three most common groups: attributive, relational and existential.

Attributive judgments(from Lat. altributum - property, sign), or judgments about the properties of something, reveal the presence or absence of certain properties (or signs) in the subject of thought. For example: “All republics of the former USSR have declared their independence”; "The Commonwealth of Independent States (CIS) is fragile." Since the concept expressing a predicate has content and scope, attributive judgments can be considered in two ways: meaningful and voluminous.

Relational judgments(from Lat. relatio - attitude), or judgments about the relationship of something to something, reveal the presence or absence of a thought object of this or that relationship to another object (or several objects). Therefore, they are usually expressed by a special formula: x R y, where x and y are objects of thought, and R (from relatio) is the relationship between them. For example: "The CIS is not equal to the USSR", "Moscow is greater than St. Petersburg."

Examples. The proposition "All metals are electrically conductive" can be turned into the proposition "All metals are like electrically conductive bodies." In turn, the judgment "Ryazan is smaller than Moscow" can be turned into the judgment "Ryazan belongs to cities that are smaller than Moscow." Or: "Knowledge is that which is like money." In modern logic, there is a tendency to reduce relational judgments to attributive ones.

Existential judgments(from Lat. existentia - existence), or judgments about the existence of something, are those in which the presence or absence of the object of thought itself is revealed. The predicate here is expressed by the words “exists” (“does not exist”), “is” (“no”), “was” (“was not”), “will” (“will not be”), etc. For example: “Smoke without there is no fire ”,“ the CIS exists ”,“ there is no Soviet Union ”. In the process of legal proceedings, first of all, the question is decided whether the event took place: “There is a crime” (“There is no evidence”).

By the quality of the bond

The quality of a judgment is one of its most important logical characteristics. By it is meant not the actual content of the judgment, but its most general logical form - affirmative, negative or negative. This reveals the deepest essence of any judgment in general - its ability to reveal the presence or absence of certain connections and relationships between conceivable objects. And this quality is determined by the nature of the link - "is" or "is not." Depending on this, simple judgments are divided according to the nature of the ligament (or its quality) into affirmative, negative and negative.

In affirmative judgments reveal the presence of any connection between the subject and the predicate. This is expressed through the affirmative link "is" or the words corresponding to it, a dash, the agreement of words. The general formula for an affirmative proposition is “S is P”. For example: "Whales are mammals."

In negative judgments, on the contrary, reveal the absence of this or that connection between the subject and the predicate. And this is achieved with the help of the negative link “is not” or the words corresponding to it, as well as just a particle of “not”. The general formula is “S is not P”. For example: "Whales are not fish." At the same time, it is important to emphasize that the particle "not" in negative judgments certainly stands before the bundle or is implied. If it is located after the bundle and is part of the predicate (or subject) itself, then such a judgment will still be affirmative. For example: "My poems are not alive with false freedom."

denying judgments- these are judgments in which the nature of the bundle is double. For example: "It is not true that man will never leave the solar system."

By subject volume

In addition to the initial, fundamental division of simple, categorical judgments by quality, there is also their division by quantity.

The amount of judgment is its other most important logical characteristic. By quantity here we mean by no means any specific number of objects conceivable in it (for example, the number of days of the week, months or seasons, planets of the solar system, etc.), but the character of the subject, i.e. its logical scope. Depending on this, general, particular and individual judgments are distinguished.

General judgments have their own varieties. First of all, they can be distinguishing and non-releasing.

Private judgments are those in which something is expressed about a part of a group of objects. In Russian they are expressed by such words as “some”, “not all”, “majority”, “part”, “individual”, etc. In modern logic they are called “existential quantifier” and are denoted by the symbol “$” (from English exist - to exist). The formula $ x P (x) reads as follows: "There is an x ​​such that the property P (x) holds." In traditional logic, the following formula of private judgments is accepted: “Some S are (are not) P”.

Examples: "Some wars are just", "Some wars are unjust" or "Some witnesses are true", "Some witnesses are not true." The quantifier word can also be omitted here. Therefore, in order to determine whether there is a particular or general judgment, one must mentally substitute the appropriate word. For example, the adage “People tend to be wrong” does not mean that it applies to everyone. Here the concept of "people" is taken in a collective sense.

By modality

The main informative function of judgment as a form of thinking is reflection in the form of affirmation or denial of connections between objects and their features. This applies to both simple and complex judgments, in which the presence or absence of a connection is complicated by the bundles.

The modality of judgments is additional information expressed in a judgment in an explicit or implicit form about the nature of the validity of the judgment or the type of dependence between the subject and the predicate, reflecting the objective relations between objects and their features.

Complex judgments and their types.

Complex judgments are formed from several simple judgments. This is, for example, the statement of Cicero: "After all, even if acquaintance with law was a huge difficulty, then the awareness of its great benefits should have prompted people to overcome this difficulty."

Just like simple, complex judgments can be true or false. But unlike simple judgments, the truth or falsity of which is determined by their correspondence or inconsistency with reality, the truth or falsity of a complex judgment depends primarily on the truth or falsity of its constituent judgments.

The logical structure of complex judgments is also different from the structure of simple judgments. The main structural elements here are no longer concepts, but simple judgments that make up a complex judgment. At the same time, the connection between them is carried out not with the help of the ligaments "is", "is not", etc., but through the logical conjunctions "and", "or", "or", "if [...], then" and others. Legal practice is especially rich in this kind of judgments.

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

1 Connective judgments (conjunctive) are those judgments that include, as constituent parts, other judgments - conjuncts, united by a sheaf of "and". For example, "The exercise of human and civil rights and freedoms should not violate the rights and freedoms of others."

2 Separating (disjunctive) judgments - include as constituent parts of judgments - clauses, united by the link "or". For example, “The plaintiff has the right to increase or decrease the amount of the claim”.

Distinguish between a weak disjunction, when the union "or" has a connecting-separating meaning, that is, the components included in a complex judgment do not exclude each other. For example, "The sales contract can be concluded orally or in writing." A strong disjunction arises, as a rule, when logical conjunctions "either", "or" are used in an exclusive-separating sense, that is, its components exclude each other. For example, "Libel, combined with the accusation of a person of committing a grave or especially grave crime, is punishable by restraint of liberty for a term of up to three years, or arrest for a term of four to six months, or imprisonment for a term of up to three years."

Conditional (implicative) judgments are formed from two simple judgments through the logical union "if [...], then." For example, "If, after the expiration of the term of temporary work with the employee, the contract was not terminated, then he is considered accepted for a permanent job." An argument that begins in implicative judgments with the word “if” is called a basis, and a component that begins with the word “then” is called a consequence.

In conditional judgments, first of all, objective causal, spatio-temporal, functional and other connections between objects and phenomena of reality are reflected. However, in the practice of applying legislation in the form of implication, the rights and obligations of people associated with certain conditions can also be expressed. For example, "Servicemen of military units of the Russian Federation stationed outside the Russian Federation, for crimes committed on the territory of a foreign state, are criminally liable under this Code, unless otherwise provided by an international treaty of the Russian Federation" (Clause 2, Article 12 of the Criminal Code of the Russian Federation) ...

It should be borne in mind that the grammatical form "if [...] then" is not an exclusive feature of a conditional judgment, it can express a simple sequence. For example, “If the perpetrator is recognized as the person who directly committed the crime, then the instigator is the person who persuaded the other person to commit

Types of questions.

The questions can be classified according to different reasons. Let's consider the main types of issues that are most often addressed in the legal field.

1. According to the degree of expression in the text, questions can be explicit and hidden. The explicit question is expressed in language completely together with its premises and the requirement to establish the unknown. The hidden question is expressed only by its premises, and the demand to eliminate the unknown is restored after understanding the premises of the question. For example, having read the text: “More and more ordinary citizens become owners of shares, and sooner or later the day comes when there is a desire to sell them,” we will not find here clearly formulated questions. However, when comprehending what you have read, you may want to ask: "What is a stock?", "Why should they be sold?", "How to sell shares correctly?" etc. The text thus contains hidden questions.

2. By their structure, questions are divided into simple and complex. A simple question is structurally based on only one judgment. It cannot be broken down into elementary questions. A complex question is formed from simple ones with the help of logical conjunctions “and”, “or”, “if, then”, etc. For example, “Which of those present identified the criminal, and how did he react to it?”. When answering a complex question, it is preferable to break it down into simple questions. A question like: "If the weather is good, will we go on an excursion?" - does not apply to complex questions, since it cannot be divided into two independent simple questions. This is an example of a simple question. The meaning of alliances that form complex questions, therefore, is not identical with the meaning of the corresponding logical alliances, with the help of which complex true or false judgments are formed from simple true or false judgments. Questions are not true or false. They can be right or wrong.

3. According to the method of requesting the unknown, clarifying and complementary questions are distinguished. Clarifying questions (or "whether" - questions) are aimed at revealing the truth of the judgments expressed in them. In all these questions there is a particle "whether" included in the phrases "is it true", "is it really", "is it necessary", etc. For example, "Is it true that Semyonov successfully defended his thesis?", "Are there really more residents in Moscow than in Paris?" and others. Complementary questions (or "k" - questions) are designed to identify new properties of the investigated object, to obtain new information. A grammatical feature is an interrogative word such as "Who?", "What?", "Why?", "When ?", "Where?" etc. For example, "How to conclude an agreement for the provision of brokerage services?" and etc

4. According to the number of possible answers to them, questions are open and closed. An open-ended question is a question that has an indefinite set of answers. A closed question is a question for which there is a finite, most often a fairly limited number of answers. These questions are widely used in judicial and investigative practice, in sociological research. For example, the question "How does this teacher give lectures?" - an open question, since many answers can be given to it. It can be rearranged in order to "close": "How does this teacher give lectures (good, satisfactory, bad)?"

5. In relation to the cognitive goal, questions can be subdivided into key and leading ones. The question is key if the correct answer serves directly to the achievement of the goal. A question is suggestive if the correct answer somehow prepares or brings a person closer to understanding the key question, which, as a rule, turns out to be dependent on the coverage of leading questions. Obviously, there is no clear line between key and leading questions.

6. According to the correctness of the formulation, the questions are divided into correct and incorrect. A correct (from Lat. Correctus - polite, tactful, courteous) question is a question, the premise of which is true and consistent knowledge. An inappropriate question is based on the premise of a false or conflicting judgment or judgment whose meaning is undefined. There are two types of logically incorrect questions: trivially incorrect and nontrivially incorrect (from the Latin trivialis - hackneyed, vulgar, devoid of freshness and originality). A question is trivially incorrect, or meaningless, if it is expressed in sentences containing obscure (indefinite) words or phrases. An example is the following question: "Do critical metaphization with abstractions and discrediting the tendency of cerebral subjectivism to ignore the system of paradoxical illusions?"

Types of answers.

Among the answers are distinguished: 1) true and false; 2) direct and indirect; 3) short and detailed; 4) complete and incomplete; 5) precise (definite) and imprecise (uncertain).

1. True and False Answers. By semantic status, i.e. in relation to reality, the answers can be true or false. The answer is regarded as true if the judgment expressed in it is correct, or adequately reflects reality. The answer is regarded as false if the judgment expressed in it is incorrect, or inadequately reflects the state of affairs in reality.

2. Direct and indirect answers. These are two types of answers, differing in the area of ​​their search.

A direct answer is one that is taken directly from the search for answers, when constructing which one does not resort to additional information and reasoning. For example, a direct answer to the question "In what year did the Russo-Japanese war end?" there will be a judgment: "The Russo-Japanese War ended in 1904". The direct answer to the is-question "Is a whale a fish?" there will be a judgment: "No, the whale is not a fish."

An indirect answer is a response that is obtained from a broader area than the area of ​​searching for an answer, and from which the necessary information can be obtained only by an inference. So, for the question "In what year did the Russo-Japanese war end?" the following answer will be indirect: "The Russo-Japanese War ended one year before the First Russian Revolution." To the question "Is a whale a fish?" the answer will be indirect: "The whale belongs to mammals."

3. Short and detailed answers. In terms of grammatical form, the answers can be short and detailed.

Short answers are monosyllabic yes or no answers.

Expanded are answers, each of which repeats all the elements of the question. For example, to the question "Was J. Kennedy a Catholic?" can be received affirmative answers: short - "Yes"; expanded - "Yes, J. Kennedy was a Catholic." Negative answers will be as follows: short - "No"; expanded - "No, J. Kennedy was not a Catholic."

Short answers are usually given to simple questions; for complex questions, it is advisable to use detailed answers, since monosyllabic answers in this case often turn out to be ambiguous.

4. Complete and incomplete answers. In terms of the amount of information provided in the response, the answers may be complete or incomplete. The problem of completeness most often arises when answering difficult questions.

A complete answer includes information on all elements or constituent parts of the question. For example, to the difficult question "Is it true that Ivanov, Petrov and Sidorov are accomplices in the crime?" the following answer will be complete: "Ivanov and Sidorov are accomplices in the crime, and Petrov is the executor." To the difficult question "By whom, when and in connection with what was the poem" To the death of a poet "written?" the following answer is complete:

“The poem“ To the death of a poet ”was written by M.Yu. Lermontov in 1837 in connection with the tragic death of A.S. Pushkin ".

An incomplete answer includes information on individual elements or constituent parts of the question. So, to the above question "Is it true that Ivanov, Petrov and Sidorov are accomplices in the crime?" - the answer will be incomplete: "No, it is not true, Petrov is an executor."

5. Accurate (definite) and imprecise (indefinite) answers! The logical relationship between question and answer means that the quality of the answer is largely determined by the quality of the question. It is no coincidence that in polemics and in the process of interrogation, the rule operates: what is the question, so is the answer. This means that it is difficult to get a clear answer to a vague and ambiguous question; if you want to get an accurate and definite answer, then formulate an accurate and definite question.

Types of dilemmas

Conditional-dividing inferences are inferences in which one of the premises is a dividing statement, and the rest are conditional statements. Another name for conditionally dividing inferences is lemmatic, derived from the Greek word lemma - a sentence, an assumption. This name is based on the fact that these inferences consider various assumptions and their consequences. Depending on the number of conditional premises, conditional-dividing inferences are called dilemmas (two conditional premises), trilemmas (three), polylemmas (four or more). In the practice of reasoning, dilemmas are most often used.

The following main types of dilemmas can be distinguished:

- a simple constructive dilemma,

- complex constructive dilemma,

- a simple destructive dilemma,

- a complex destructive dilemma.

An example of a simple constructive dilemma (Socratic reasoning):

“If death is a transition into nothingness, then it is good. If death is a transition to another world, then it is good. Death is a transition into nothingness or into another world. Therefore, death is a blessing. "

Simple constructive (assertive) dilemma:

If A, then C.

If B, then C.

An example of a complex constructive dilemma:

The young Athenian turned to Socrates for advice: should he marry? Socrates replied: “If you come across a good wife, then you will be a happy exception, if a bad one, then you will be like me, a philosopher. But you will get a good or a bad wife. Therefore, you either be a happy exception, or a philosopher. "

Complex constructive dilemma:

If A, then B.

If C, then D.

An example of a simple destructive dilemma:

“In today's world, if you want to be happy, you have to have a lot of money. However, it has always been the case that if you want to be happy, you need to have a clear conscience. But we know that life is arranged in such a way that it is impossible to have both money and conscience at the same time, i.e. either there is no money, or there is no conscience. Therefore, give up hope for happiness. "

Simple destructive (denying) dilemma:

If A, then B.

If A, then C.

Wrong B or Wrong C.

False A.

An example of a complex destructive dilemma:

“If he is smart, then he will see his mistake. If he is sincere, then he confesses to her. But he either does not see his mistake, or does not admit it. Therefore, he is either not smart or not sincere. "

Complex destructive dilemma:

If A, then B.

If C, then D.

Not-B or Not-D.

Not-A or not-C.

An example of complete inductive inference.

All convictions are issued in a special procedural order.

All acquittals are issued in a special procedural order.

Convictions and acquittals are court decisions.

All court decisions are issued in a special procedural order.

This example reflects the class of objects - court decisions. All (both) of its elements have been specified. The right side of each of the premises is valid with respect to the left. Therefore, the general conclusion, which is directly related to each case separately, is objective and true.

Incomplete induction is called an inference that, on the basis of the presence of certain recurring features, classifies an object as belonging to the class of similar objects that also have such a feature.

Incomplete induction is often used in a person's everyday life and scientific activity, as it allows making a conclusion based on the analysis of a certain part of a given class of objects, saves a person's time and energy. At the same time, one should not forget that as a result of incomplete induction, a probabilistic conclusion is obtained, which, depending on the type of incomplete induction, will fluctuate from less probable to more probable (11).

The above can be illustrated by the following example.

The word "milk" changes in cases. The word "library" changes in cases. The word "doctor" changes in cases. The word "ink" changes in cases.

The words "milk", "library", "doctor", "ink" are nouns.

Probably all nouns change in case.

Depending on the tog

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LECTURE TEXTS

TO THE COURSE OF THE DISCIPLINE "LOGIC"

Topic 1. SUBJECT AND MEANING OF LOGIC

1.1. The concept of "logic", its main meanings. The place of logic in the system of the sciences of thinking.

Term "logics" comes from the Greek word logos, which means "thought", "word", "mind", "regularity", and is used both to denote a set of rules that govern the process of thinking, and to denote the science of the rules of reasoning and those forms in which it is carried out. In addition, this term is used to denote any patterns ("logic of things", "logic of events").

The study of thinking occupies one of the central places in all philosophical teachings, both past and present. Thinking is studied not only by logic, but also by a number of other sciences - philosophy, physiology, cybernetics, linguistics, each highlighting its own aspect of study:

Philosophy- studies the relationship between matter and thinking.

Sociology- analyzes the historical development depending on the social structures of society.

Cybernetics- studies thinking as an information process.

Psychology- studies the mechanisms of realization of mental acts, including cerebral ones, and understands thinking as a cognitive activity.

The role of thinking in cognition.

From the first days of his life, a person is involved in the process of knowing the world around him. He learns the individual signs of objects and phenomena that are reflected in sensations ; integral objects and phenomena in their direct given to man are presented in the perception ; visible and invisible to the human eye connections and relationships between objects and phenomena allows you to open thinking . In a broad sense, a person's thinking is understood as his active cognitive activity with an internal process of planning and regulation of external activities. To understand how a person thinks means to understand how he sees (represents, reflects) the world around him, himself in this world and his place in it, as well as how he uses knowledge about the world and about himself to control his own behavior.

Cognition there is the construction of the semantic (ideal) content of the world in the minds of people. The surrounding world and its properties are revealed in the process of cognition. Practice is one of the elements of knowledge. In practice, people are faced with various properties of objects and phenomena. Cognition has two main stages: sensual and rational.

All its material mental activity receives from only one source - from sensory knowledge. Sensory cognition has three main forms: sensation, perception and representation... Through sensations and perceptions, thinking is directly connected with the external world and is its reflection. The correctness (adequacy) of this reflection is continuously tested in the process of practical transformation of nature and society.

Sensation- a subjective image of the objective world, the transformation of the energy of external irritation into a fact of consciousness.

Any empirical knowledge begins with living contemplation, sensory perception. The forms of sensory perception are reflections of individual properties of objects or phenomena that directly affect the sense organs. Each item has not one, but many properties. In sensations, various properties of objects are reflected.

Perception- this is a reflection in the human mind of integral complexes of properties of objects and phenomena of the objective world with their direct impact at a given moment on the sense organs.

Representation- this is a sensory image of an object that is not perceived at the moment, but which was previously perceived in one form or another. The performance can be reproductive (for example, everyone now has an image of their home, their workplace, images of some acquaintances and relatives who we do not see now), creative, including fantastic. Through sensory perception, a person discovers the appearance of an object, but not its essence. The laws of the world, the essence of objects and phenomena, a person learns in common in them through abstract thinking, which represents the world and its processes deeper and more fully than sensory perception. The transition from sensory perception to abstract thinking is a qualitatively different level in the process of cognition. This is a transition from the primary presentation of facts to the knowledge of laws.

The main forms of the abstract, i.e. abstracted from the directly given reality of thinking, are concepts, judgments and inferences.

Concept- a form of thinking that reflects the essential properties, connections and relationships of objects and phenomena, expressed by a word or a group of words. Concepts can be general and singular, concrete and abstract.

Judgment - a form of thinking that reflects connections between objects and phenomena; affirmation or denial of something. Judgments can be true or false.

Inference- a form of thinking in which a certain conclusion is made on the basis of several judgments. It is a series of logically related statements from which new knowledge is derived.

Example: All those present at the lecture are students. Olya is present at the lecture (2 judgments). Olya is a student (inference).

Distinguish inferences inductive, deductive and Similarly.

In the process of logical cognition, a person seeks to achieve the truth. Logical truth, or truth, is the correspondence of an inference to those rules of thinking that are established for it. This will mean that the premises and the conclusion following from them are combined logically "correctly", i.e. correspond to the truth criterion established for a given logical system. The task of any logical system is to show what are the rules for combining individual meanings and to what conclusions this combination leads. These conclusions will be what is called logical truth.

An essential feature of abstract thinking is its inextricable connection with language, since the laws of origin, combination, and expression of linguistic meanings are identical to the functioning of logical meanings. This means that any phrase, sentence or combination of sentences has a certain logical meaning.

1.3. The main stages of the development of logic

The emergence of logic as a theory was preceded by the practice of thinking going back thousands of years.

History testifies that individual logical problems arise in the mind's eye of a person already over 2.5 thousand years ago - first in Ancient India and Ancient China. Then they get more complete development in Ancient Greece and Rome. Only gradually do they add up to a more or less harmonious system and take shape as an independent science.

Reasons for the emergence of logic... First, the origin and initial development in Ancient Greece of sciences (VI century BC), primarily mathematics. Born in the fight against mythology and religion, science was based on theoretical thinking, involving inference and proof. Hence - the need to study the nature of thinking itself as a form of knowledge. Logic arose, first of all, as an attempt to identify and explain the requirements that scientific thinking must satisfy in order for its results to correspond to reality. Another reason is the development of oratory, including judicial art, which flourished under the conditions of the ancient Greek pole democracy.

Formal logic has gone through two main stages in its development.

First stage associated with the works of the ancient Greek philosopher and scientist Aristotle (384-322 BC), who was the first to give a systematic presentation of logic. Aristotle's logic and all pre-mathematical logic are usually called "traditional" formal logic. Traditional formal logic included and includes such sections as concept, judgment, inference (including inductive), laws of logic, proof and refutation, hypothesis. Aristotle gave a classification of the most general concepts - the classification of judgments, the fundamental laws of thinking - the law of identity, the law of the excluded third. The logic itself was further developed both in Greece and in other countries.

Medieval scholastics made a significant contribution to the development of logic. The Latin terminology introduced by them is still preserved.

During the Renaissance, logic was in crisis. It was regarded as the logic of "artificial thinking", which was opposed to natural thinking based on intuition and imagination.

A new stage in the development of logic begins in the 17th century. This is due to the creation within its framework, along with deductive logic, of inductive logic. The need for such knowledge was most fully realized and expressed in his writings by the outstanding English philosopher and natural scientist. Francis Bacon(1561-1626). He became the founder of inductive logic, writing, in contrast to the old "Organon" of Aristotle, "New Organon ...".

Inductive logic was later systematized and developed by the English philosopher and scientist John Stuart Mill(1806-1873) in his two-volume work "System of syllogistic and inductive logic".

The needs of scientific knowledge not only in the inductive, but also in the deductive method in the 17th century. most fully embodied by the French philosopher and scientist Rene Descartes(1596-1650). In his main work "Discourse on the method ...", based on data, primarily mathematics, he emphasizes the importance of rational deduction.

Followers of Descartes from the monastery at Port Royal A. Arno and P. Nicole created the work "Logic, or the Art of Thinking". It became known as the "Logic of Port Royal" and was used for a long time as a textbook on this science.

Second phase - this is the appearance mathematical (or symbolic) logic.

Growing advances in the development of mathematics and the penetration of mathematical methods into other sciences in the second half of the 17th century. strongly put forward two fundamental problems. On the one hand, this is the use of logic to develop the theoretical foundations of mathematics, and on the other, the mathematization of logic itself as a science.

The largest German philosopher and mathematician G. Leibniz(1646-1716) is rightfully considered the founder of mathematical (symbolic) logic, since it was he who used the formalization method as a research method. However, the most favorable conditions for powerful development of mathematical (symbolic) logic received in the works D. Boulle, E. Schroeder, P.S. Poretsky, G. Frege and other logicians. By this time, the mathematization of sciences had made significant progress, and in mathematics itself new fundamental problems of its justification arose.

This opened a new, modern stage in the development of logical research. Perhaps the most important distinguishing feature of this stage is the development and use of new methods for solving traditional logical problems. This is the development and application of the so-called formalized language - the language of symbols, ie, alphabetic and other signs (hence the most common name for modern logic - "symbolic").

There are two types of logical calculus: propositional calculus and calculus of predicates. In the first case, abstraction from the conceptual structure of judgments is allowed, and in the second, this structure is taken into account and, accordingly, the symbolic language is enriched, supplemented with new signs.

Formation of dialectical logic... At one time, even Aristotle posed and tried to solve a number of fundamental problems dialectical logic- the problem of reflecting real contradictions in concepts, the problem of the relationship between the individual and the general, the thing and the concept of it, etc. Elements of dialectical logic gradually accumulated in the works of subsequent thinkers and were especially clearly manifested in the works Bacon, Hobbes, Descartes, Leibniz... However, as an independent logical science, qualitatively different from formal logic in its approach to thinking, dialectical logic began to take shape only at the end of the 18th - beginning of the 19th centuries.

The first to try to introduce dialectics into logic was the German philosopher I. Kant(1724-1804). Kant believed that logic is "a science that expounds in detail and strictly proves only the formal rules of all thinking ...".

But in this undoubted advantage of logic, Kant discovered its main drawback - limited possibilities as a means of real knowledge and verification of its results. Therefore, along with "general logic", which Kant for the first time in its history also called "formal logic" (and this name has stuck with it up to the present time), a special, or "transcendental logic" is needed. He saw the main task of this logic in the research of such, in his opinion, really basic forms of thinking, such as categories: "We cannot think of a single object except with the help of categories ...". They serve as a condition for any experience, therefore they are of an a priori, pre-experienced character. These are the categories of space and time, quantity and quality, cause and effect, necessity and chance, and other dialectical categories, the use of which supposedly does not obey the requirements of the laws of identity and contradiction.

Another German philosopher, G. Hegel(1770-1831). In his seminal work "Science of Logic", he revealed the fundamental contradiction between the available logical theories and the actual practice of thinking, which by that time had reached significant heights. The means of resolving this contradiction was the creation by him in a peculiar, religious-mystical form of a system of new logic. Its focus is on the dialectic of thinking in all its complexity and contradictions.

The growing needs of scientific and technological progress determine the further intensive development of modern logic.

Topic 2. The language of logic

The subject of study of logic is the forms and laws of correct thinking. Thinking is a function of the human brain that is inextricably linked with language.

2.1. The relationship between language and thinking. The concept of sign systems.

Cognitive thinking, studied by logic, is always expressed in language, therefore logic considers thought in its linguistic expression. The functions of a natural language are numerous and multifaceted.

Language- a means of everyday communication between people, a means of communication in scientific and practical activities. The language is also characterized by such functions: store information, be a means of expressing emotions, be a means of knowledge. Language is a symbolic information system, a product of human spiritual activity. The accumulated information is transmitted using characters (words) of the language.

Speech can be oral or written, sound or non-sound (for the deaf and dumb), external (for others) or internal, speech expressed using natural or artificial language. With the help of a scientific language, which is based on a natural language, the provisions of all sciences are formulated.

Artificial languages ​​of science emerged on the basis of natural languages . These include the languages ​​of mathematics, symbolic logic, chemistry, physics, as well as algorithmic programming languages ​​for computers, which are widely used in modern computers and systems.

Word and concept. Name... The ability to cognize the external world by means of ideas reflecting objects in their general and essential features creates a generally valid logical form of thinking - concept... Without a concept, it is impossible to formulate laws and single out the subject area of ​​science. The concept helps to distinguish certain classes of things and distinguish them from each other. The concept appears as the result of abstraction, that is, mentally highlighting the essential properties of things and their generalization through distinctive features.

Language serves to express thoughts. Names not only designate certain objects, but also express this or that thought. This thought (more precisely, the form of thought) is called a concept.

Concept there is a form of thought expressed by a name. Our everyday and professional conversations, speeches, disputes consist of words and sentences.

Among the words we use, the names are the most important, since they make up most of the words.

Name is an expression of language that denotes a separate object, a set of objects, a property or a relation.

Names are divided into: 1) simple, complex, descriptive; 2) own;3) are common... Each name has a meaning, or meaning. The meaning, or meaning of a name, is the way in which the name denotes an object, that is, the information about the object contained in the name. Different expressions denoting the same subject have the same meaning, or meaning.

In logic, expressions are distinguished, which are nominal functions, and expressions, which are propositional functions. Named function is an expression that, when variables are replaced by constants, turns into a designation of an object. This is the name of an expression that contains a variable and turns into a true or false statement when substituting the name of an object from a certain subject area instead of a variable.

In logical analysis, language is considered as a sign system.

Sign is a material object used in the process of cognition or communication as a representative of an object.

It is possible to distinguish signs of the following three types: 1) signs - indices; 2) sample signs; 3) signs are symbols.

Index signs associated with the objects they represent, or effects with causes.

Sample marks are those signs that in themselves give information about the objects they represent (map of the area, map-drawing), since they are in relation to similarity with the designated objects.

Symbols not causally related and not similar to their representation of objects. Logic examines signs of the latter kind.

To the main symbols replacing the main concepts of logic, the concept of a subject, or an object of thought (logical subject) and a predicate, i.e. signs of the object of thought, inherent or not inherent in it (logical predicate), include S and P... The concepts of "subject" and "predicate" are also used in philosophy, so from the very beginning it is necessary to establish, albeit not so radical, but still existing differences between their philosophical and logical meanings. In philosophy, the "subject" is both an individual person and thinking humanity, society as a whole, that is, that which opposes the "object" - nature, the world as a whole. In logic, "subject" is the subject of thought, what our consciousness, our attention, intellect, reason is directed to, what reasoning is about, this is a logical subject of judgment. It can be any concept that reflects any real or imaginary, material or ideal "object". Thus, the subject of thought can be anything.

"Predicate" in philosophy and logic almost coincide in meaning, it is any feature, inherent or not inherent in this or that subject, in logic, of course, the subject of thought.

S - a symbol for designating the subject of judgment (subject of thought, logical subject).

P - the symbol of the predicate of the judgment (logical predicate), i.e. a concept that reflects a feature inherent or not inherent in the object of thought (subject).

M - the middle term of inference, the general length of the initial judgments concept.

"Is" - "is not" (essence - not essence, etc.) - a logical connection between the subject and the predicate of the judgment, sometimes expressed by a simple dash between "S" and "P".

R is the symbol of any relationship.

A (a) is a symbol of a generally affirmative judgment ("All students are students").

E (e) is a symbol of a generally negative judgment (“All students in this group are not athletes”, or, which is the same thing, “No student in this group is an athlete”).

I (i) - a symbol of a private affirmative judgment ("Some students are excellent students").

O (o) is a symbol of a partial negative judgment (“Some students are not excellent students”).

V is the symbol of the quantifier of generality (universality), in language it is expressed by the word "all", "for everyone", etc.

I - the symbol of the quantifier of existence, in the language it is expressed by the word "some", "there are such", "many", etc.

/ \ - symbol, or sign of the connecting logical union "and" (conjunction).

V - symbol (sign) of the dividing logical union "or" (disjunction).

-> - symbol of the conditional logical union "if .. then ..." (implication).

<-->- a symbol of the logical union of identity, equivalence: “if and only if”, “if and only if” (equivalent).

"Not" is a negative particle, it can also be expressed by a line above the sign, for example: B, C.

A symbol to indicate a need.

A symbol to denote an opportunity.

On the basis of natural languages, artificial languages ​​of science arose. These include the languages ​​of mathematics, symbolic logic, chemistry, physics, as well as algorithmic programming languages ​​for computers, which are widely used in modern computers and systems.

Names are linguistic expressions, the substitution of which in the formula "S is P" instead of the variables S and P gives a meaningful sentence.

The names are, for example, "starry night", "Volga", "Tambov" and "evening twilight". Substitution of these expressions into the indicated form gives meaningful (although not necessarily true) sentences: "Tambov is the Volga", "Evening twilight is a starry night", "A starry night is the Volga", etc.

Suggestion (utterance) is a linguistic expression that is true or false.

Functor is a linguistic expression that is neither a name nor an utterance and serves to form new names or utterances from existing ones.

Topic 3. Basic laws of logic

3.1. The concept of "logical law"

The first three of these laws were identified and formulated by Aristotle, and the law of sufficient reason was formulated by G. Leibniz.

The study of these laws is necessary and important for understanding the complex deep processes that naturally occur in thinking, regardless of our awareness of them and will, as well as for the use of these laws in the practice of mental activity. Violation of laws leads to logical contradictions and the inability to distinguish truth from falsehood.

Identity law establishes the requirement of definiteness of thinking: using a term in the process of thinking, we must understand by it something definite. Therefore, in the reasoning, it is necessary to leave the concepts and judgments the same in content and meaning. This requirement is maintained if each transformation is canceled in the opposite way (null transformation).

The invariability of thought in the course of reasoning is fixed by the formula A is A or A≡A, or not A is not A. The objective basis of the law is in temporary equilibrium, the rest of any body or process.

Even constant movement, change makes it possible to recognize and identify objects. This objective property of a thing, of an event to maintain identity, one and the same quality, must be reflected by thinking, which must grasp the constancy of the object. The law of identity requires that concepts and judgments are unambiguous, without ambiguities and ambiguities.

From this brief overview it is clear that the law of identity is universal in the sense of covering all forms of thinking without exception, all thought in general.

Requirements of the law of identity and logical errors due to their violation.

Certain requirements follow from the law of identity that is objectively operating in our thinking.

These are logical norms, attitudes, prescriptions or rules that are formulated by people themselves on the basis of the law and which must be observed in order for thinking to be correct, leading to truth. They can be summarized as follows:

1) Each concept, judgment, etc. must be used in the same definite sense and keep it in the process of the whole reasoning.

The following is connected with this requirement.

2) Different thoughts cannot be identified and identical thoughts cannot be taken for different.

Demanding definiteness, unambiguousness of thought, the law of identity is at the same time directed against any fuzziness, inaccuracy, blurring of our concepts, etc.

In cases where the requirements of the law of identity are violated, numerous logical errors arise. They are called differently: " amphibole"(Ambiguity, that is, the use of the same homonym word simultaneously in different senses)," confusion of concepts "," confusion in concepts "," substitution of one concept for another "( equivocation), "substitution of thesis", etc.

The meaning of the law of identity. Knowledge of the law of identity and its use in the practice of thinking is of fundamental importance, since it allows you to consciously and clearly separate the correct reasoning from the wrong one, to find logical errors - ambiguity, substitution of concepts, etc. - in the reasoning of other people and avoid your own.

In any speech - written or oral - one should, in accordance with the law of identity, achieve clarity of presentation, and it involves the use of words and expressions in the same sense, understandable to others, and in natural combinations with other words.

It is very important to comply with the requirements of the law of identity in discussions, disputes, etc. In order for the dispute to not be pointless, it is always necessary to accurately determine the subject of the dispute and precisely clarify the key concepts in it. For equivalent concepts, you can and should use synonymous words. It should only be remembered that synonymy is relative (words that are synonyms in one respect, are not them in another). And under the guise of synonyms, completely different concepts are sometimes used. If the words homonyms are used, then it is required to find out exactly the meaning in which they are taken in this case.

The law of consistency expresses the requirement for the consistency of thinking and reflects the qualitative definiteness of objects. From the point of view of this remark, an object cannot have mutually exclusive properties, that is, it is impossible, at the same time, the presence and absence of any property of the object.

The formula of the law says: it is not true that A and not A are simultaneously true.

The law of consistency is directly related to the law of identity. If the law of identity speaks of a certain equality of the object of thought to itself, then the law of consistency indicates that “this” object of thought must necessarily differ from all other objects. Thus, the law of consistency has its own content. It is expressed in the following: one and the same object at the same time and in the same sense cannot be attributed opposite signs. If opposite signs are attributed to the same object, then one of them, in any case, is attributed falsely.

This cannot be the truth of judgment at the same time: this person is a good specialist - this person is a bad specialist.

The objective content of the law in the reflection by thinking of special binomial features of reality itself. These opposite signs, or constructs, allow you to classify phenomena and highlight positive and negative phenomena. Without doing this, no distinction can be drawn from which mental activity begins. The logical source of contradiction is an erroneous starting position; the result of thoughtlessness and ignorance of the matter; undeveloped, undisciplined thinking; ignorance and the desire to deliberately confuse the matter.

At the same time, opposite judgments can be true in the following cases:

1) if we are talking about different signs of one item;

2) if we are talking about different objects with one characteristic;

3) if we are talking about one subject, but it is considered at different times and in different ways.

Scope of the law of consistency. This law is, first of all, a generalization of the practice of operating judgments. It reflects the natural relationship between two judgments - positive and negative, the relationship of their incompatibility in truth: if one is true, then the other is certainly false.

Judgments are divided into positive and negative, and they, in turn, into true and false, this explains the universal nature of the law of non-contradiction. Since complex judgments are formed from simple judgments, the law of non-contradiction also applies here if they are in a denial relation.

This law also applies to concepts, namely the relationship between them. This is a relationship of incompatibility.

So, if the forest is "coniferous", then it cannot be "deciduous" (relation of subordination); if a person is "generous", then he cannot be at the same time "generous" (the attitude of contradiction) or "stingy" (the attitude of the opposite).

The law of consistency is also found in inferences. On it are based, for example, direct inferences through the transformation of judgments. This operation is possible only because the object of thought cannot simultaneously belong and not belong to the same class of objects. Otherwise, there will be a logical contradiction. In inferences through the relation of judgments in a logical square, the action of the law of non-contradiction is reflected in the fact that if any judgment is true, then the contradicting or opposite to it will be false. In other words, they cannot be true at the same time.

Finally, the law of contradiction operates in the proof. It underlies one of the rules of the grounds of proof: they must not contradict each other. Without the operation of this law, refutation would have been impossible. Having proved the truth of one thesis, it is not possible to conclude that an opposite or contradicting thesis is false.

The requirement of consistency of thought and its violation in the practice of thinking. The operation of the objective law of consistency in thinking makes a person an important requirement - consistency in his reasoning, in the connections between thoughts. For our thoughts to be true, they must be consistent, consistent. Or: in the process of any reasoning, one cannot contradict oneself, reject one's own statements, which are recognized as true.

A variety of logical errors - "logical contradictions" are associated with the violation of the requirements of the law of consistency.

The meaning of the law of consistency. It is especially important to take into account the operation of the law of contradiction in science, since any scientific reasoning - more or less detailed, detailed, mutually exclusive thoughts can be in different places and it is simply difficult to detect them. It is all the more difficult to do this if the reasoning is divided in time: what was asserted at one time, can be unnoticed by the speaker himself, denied at another. But from this logical contradictions do not lose their harm. They represent an intellectual "slag" that clogs our reasoning and requires constant cleansing them so that we can successfully move towards the truth. That is why science attaches fundamental importance to the prevention or elimination of logical contradictions in it.

One of the most important conditions for building a scientific system is the consistency of the initial data ("consistency of the system of axioms").

Another condition is the consistency of the theoretical constructions arising from them ("the consistency of the theoretical system itself"). If any contradiction of the logical order is found in science, then they strive to eliminate it in every possible way, as an obstacle to the knowledge of the truth.

Logical contradictions are intolerable in everyday speech. A person ceases to be respected if he says one thing on the same occasion today and another tomorrow. This is a man without principles.

The excluded third law makes stronger demands on judgments and requires not to shy away from recognizing the truth of one of the conflicting statements and not to look for something third between them.

The law of the excluded third is denoted by the formula A is either B or not B. The meaning of this formula is as follows. Whatever the object of our thought (A), this object either has a known property (B), or does not have it. It is impossible for it to be false both that the object A has property B, and that the object does not have this property. Truth is necessarily found in one of two conflicting propositions. No third judgment about the relationship of A to B and not B can be true. Therefore, there is a dichotomy here, according to which, if one of the two is true, then the other is false, and vice versa.

This law and its action are not reducible to the future, where the event will either take place or not. The law is alternative in characterizing things, hypotheses and ways of solving problems, requires distinguishing different approaches and determining the true one.

The law of the excluded middle and the law of non-contradiction are related. Both of them do not allow conflicting thoughts to exist. But there are also differences between them. The law of non-contradiction expresses the relationship between opposing judgments. For example: "This paper is white." - "This paper is black." The law of the excluded third expresses the relationship between conflicting judgments. For example: "This paper is white." - "This paper is not white." Because of this, if the law does not contradict, both judgments cannot be true at the same time, but they can be false at the same time, and the third judgment will be true - “This paper is red”. In the case of the law of the excluded third, both judgments cannot be simultaneously false, one of them will be necessarily true, the other false, and no third, middle judgment is possible. If judgments contradicting in form do not refer to a single object, but to a class of objects, when something is affirmed or denied in relation to each object of a given class and the same is denied in relation to each object of a given class, then the truth relations between them are established according to the rules of "logical square ”. When one of the judgments asserts something regarding the entire class of objects or phenomena, and the other judgment denies the same regarding some of the objects or phenomena of the same class, then one of these judgments will be necessarily true, the other will be false, and the third is not given. For example: “All fish breathe with gills” and “Some fish do not breathe with gills”. Both of these judgments can be neither true nor false at the same time.

Excluded Third Law Requirements and Their Violations. On the basis of this law, certain requirements for thinking can be formulated. A person often faces a dilemma: to choose not from identical, but from mutually denying statements. The law of the excluded third makes the requirement of choice - one of the two - according to the principle "either - or", tetrium non datur (the third is not given). It means that when solving an alternative question, one cannot evade a definite answer; you cannot look for something intermediate, middle, third.

Significance of the law of the excluded third. This law cannot indicate exactly which of the two conflicting judgments is true. But its significance lies in the fact that it establishes for us quite definite intellectual boundaries within which the search for truth is possible. This truth is contained in one of two statements that deny each other. It makes no sense to look outside these limits. The very choice of one of the judgments as true is provided by the means of one or another science and practice.

Logic is one of the most ancient subjects, which stands next to philosophy and sociology and is an essential general cultural phenomenon from the very beginning of its emergence. The role of this science in the modern world is important and multifaceted. Those who possess knowledge in this area can conquer the whole world. It was believed that this is the only science capable of finding compromise solutions in any situation. Many scientists attribute the discipline to others, but in turn, refute this possibility.

Naturally, over time, the orientation of logical research changes, methods are improved and new trends appear that meet scientific and technical requirements. This is necessary because every year society is faced with new problems that cannot be solved with outdated methods. The subject of logic studies the thinking of a person from the side of those laws that he uses in the process of knowing the truth. In fact, since the discipline we are considering is very multifaceted, it is studied using several methods. Let's take a look at them.

Etymology of logic

Etymology is a branch of linguistics, the main purpose of which is the origin of a word, its study from the point of view of semantics (meaning). "Logos" in translation from Greek means "word", "thought", "knowledge". Thus, we can say that logic is a subject that studies thinking (reasoning). However, psychology, philosophy and physiology of nervous activity, one way or another, also study thinking, but can we say that these sciences study the same thing? Rather, the opposite is true - in a sense, they are opposite. The difference between these sciences is the way of thinking. Ancient philosophers believed that a person's thinking is diverse, because he is able to analyze situations and create an algorithm for performing certain tasks to achieve a specific goal. For example, philosophy as a subject is rather just a discussion about life, about the meaning of being, while logic, in addition to idle reflections, leads to a certain result.

Reference Method

Let's try to refer to dictionaries. Here the meaning of this term is somewhat different. From the point of view of the authors of encyclopedias, logic is a subject that studies the laws and forms of human thinking from the surrounding reality. This science is interested in how “living” true knowledge functions, and in search of answers to their questions, scientists do not turn to each specific case, but are guided by special rules and laws of thinking. The main task of logic as a science of thinking is to take into account only the method of obtaining new knowledge in the process of cognizing the surrounding world, without associating its form with a specific content.

The principle of logic

The subject matter and meaning of logic is best seen through a concrete example. Let's take two statements from different fields of science.

1. “All stars have their own radiation. The sun is a star. It has its own radiation. "
2. Any witness must tell the truth. My friend is a witness. My friend is obliged to tell the truth.

If you analyze it, you can see that in each of them two reasoning explains the third. Although each of the examples belongs to different areas of knowledge, the way in which the constituent parts of the content are related in each of them is the same. Namely: if an object has a certain property, then everything that concerns this quality has a different property. Result: The item in question also has this second property. These causal relationships are commonly called logic. This relationship can be observed in many situations in life.

Let's turn to history

To understand the true meaning of this science, you need to know how and under what circumstances it arose. It turns out that the subject of logic as a science arose in several countries almost simultaneously: in Ancient India, in Ancient China and in Ancient Greece. If we talk about Greece, then this science arose during the disintegration of the clan system and the formation of such strata of the population as merchants, landowners and artisans. Those who ruled Greece infringed on the interests of almost all segments of the population, and the Greeks began to actively express their positions. In order to resolve the conflict peacefully, each side used its own arguments and arguments. This gave impetus to the development of such a science as logic. The subject was used very actively, because it was very important to win the discussions in order to influence decision-making.

In ancient China, logic arose during the golden age of Chinese philosophy, or, as it was also called, the period of "struggling states." Similar to the situation in Ancient Greece, there also flared up a struggle between the wealthy strata of the population and the authorities. The first wanted to change the structure of the state and abolish the transfer of power by hereditary means. During such a struggle, in order to win, it was necessary to gather around him as many supporters as possible. However, if in Ancient Greece this served as an additional incentive for the development of logic, then in Ancient China it was quite the opposite. After the Qin kingdom nevertheless became dominant, and the so-called cultural revolution took place, the development of logic at this stage

e stopped.

Considering that in different countries this science arose precisely during the period of struggle, the subject and meaning of logic can be characterized as follows: it is the science of the sequence of human thinking, which can positively influence the solution of conflict situations and disputes.

The main subject of logic

It is difficult to single out one definite meaning that would generally characterize such an ancient science. For example, the subject of logic is the study of the laws of deriving correct certain judgments and statements from certain true circumstances. This is how Friedrich Ludwig Gottlob Frege characterized this ancient science. The concept and subject of logic was also studied by Andrei Nikolaevich Schuman, a well-known modern logician. He believed that it was the science of thinking, which explores different ways of thinking and models them. In addition, the object and subject of logic is, of course, speech, because logic is realized only through conversation or discussion, and it does not matter at all whether aloud or "inwardly."

The above statements indicate that the subject of the science of logic is the structure of thinking and its various properties that separate the sphere of abstract logical, rational thinking - forms of thinking, laws, the necessary relationships between structural elements and the correctness of thinking to achieve truth.

The process of seeking truth

In simple terms, logic is a thought process of the search for truth, because on the basis of its principles, the process of the search for scientific knowledge is formed. There are various forms and methods of using logic, and they are all combined into a theory of the derivation of knowledge in various fields of science. This is the so-called traditional logic, within which there are more than 10 different methods, but the deductive logic of Descartes and the inductive logic of Bacon are still considered the main ones.

Deductive logic

We all know the deduction method. Its use is somehow connected with such science as logic. The subject of Descartes' logic is a method of scientific knowledge, the essence of which lies in the strict derivation of new ones from certain provisions that were previously studied and proved. He was able to explain why, since the initial statements are true, then the derived ones are also true.

For deductive logic, it is very important that there are no contradictions in the initial statements, since later they can lead to incorrect conclusions. Deductive logic is very precise and does not tolerate assumptions. All postulates that are used are usually based on verified data. This one has the power of persuasion and is used, as a rule, in the exact sciences such as mathematics. Moreover, the very method of finding the truth is not questioned, but the very method of finding the truth is being studied. For example, the well-known Pythagorean theorem. How can you question its correctness? Rather, on the contrary, it is necessary to learn a theorem and learn how to prove it. The subject "Logic" studies exactly this direction. With its help, with knowledge of certain laws and properties of an object, it becomes possible to derive new ones.

Inductive logic

We can say that the so-called inductive logic of Bacon practically contradicts the basic principles of deductive. If the previous method is used for exact sciences, then this one is for natural ones, in which logic is needed. The subject of logic in such sciences: knowledge is obtained through observation and experiment. There is no place for precise data and calculations. All calculations are made only purely theoretically, with the aim of studying an object or phenomenon. The essence of inductive logic is as follows:

1. Carry out constant observation of the object that is being investigated, and create an artificial situation that could arise purely theoretically. This is necessary to study the properties of certain objects that cannot be learned in natural conditions. This is a prerequisite for learning inductive logic.
2. Based on observations, collect as many facts as possible about the object under study. It is very important to note that since the conditions were created artificially, the facts can be distorted, but this does not mean that they are false.
3. Summarize and systematize the data obtained during the experiments. This is necessary to assess the situation that has arisen. If the data turns out to be insufficient, then the phenomenon or object must be placed again in another artificial situation.
4. Create a theory to explain the data obtained and predict their further development. This is the final stage, which serves to summarize. The theory can be formulated without taking into account the actual data obtained, however, it will nevertheless be accurate.

For example, on the basis of empirical research on natural phenomena, oscillations of sound, light, waves, etc., physicists have formulated the proposition that any phenomenon of a periodic nature can be measured. Of course, for each phenomenon, separate conditions were created and certain calculations were carried out. Depending on the complexity of the artificial situation, the readings varied significantly. This is what made it possible to prove that the periodicity of the oscillation can be measured. Bacon explained scientific induction as a method of scientific cognition of cause-and-effect relationships and a method of scientific discovery.

Causal relationship

From the very beginning of the development of the science of logic, much attention was paid to precisely this factor, which affects the entire process of research. Causality is a very important aspect in the learning process of logic. A reason is a certain event or object (1), which naturally influences the emergence of another object or phenomenon (2). The subject of the science of logic, formally speaking, is to find out the reasons for this sequence. Indeed, from the above, it turns out that (1) is the cause of (2).

An example can be given: scientists who study outer space and the objects that are there have discovered the phenomenon of a "black hole". This is a kind of cosmic body, the gravitational field of which is so great that it is capable of absorbing any other object in space. Now let's find out the cause-and-effect relationship of this phenomenon: if any cosmic body is very large: (1), then it is capable of absorbing any other (2).

Basic methods of logic

The subject of logic briefly studies many areas of life, but in most cases the information obtained depends on the logical method. For example, analysis is called the figurative division of the object under study into certain parts, in order to study its properties. Analysis, as a rule, is necessarily associated with synthesis. If the first method divides the phenomenon, then the second, on the contrary, connects the received parts to establish a relationship between them.

Another interesting subject of logic is the abstraction method. This is the process of mentally separating certain properties of an object or phenomenon in order to study them. All these techniques can be classified as cognitive methods.

There is also a method of interpretation, which consists in the knowledge of the sign system of certain objects. Thus, objects and phenomena can be given a symbolic meaning that will facilitate understanding of the essence of the object itself.

Modern logic

Modern logic is not a teaching, but a reflection of the world. As a rule, this science has two periods of formation. The first begins in the Ancient World (Ancient Greece, Ancient India, Ancient China) and ends in the 19th century. The second period begins in the second half of the 19th century and continues to this day. Philosophers and scientists of our time do not stop studying this ancient science. It would seem that all its methods and principles have long been studied by Aristotle and his followers, but every year logic as a science, a subject of logic, as well as its features continue to be studied.

One of the features of modern logic is the spread of the subject of research, which is due to new types and ways of thinking. This led to the emergence of such new types of modal logic as logic of change and causal logic. It has been proven that such models differ significantly from those already studied.

Modern logic as a science is used in many spheres of life, such as engineering and information technology. For example, if you consider how a computer is arranged and works, you can find out that all programs on it are executed using an algorithm, where logic is involved in one way or another. In other words, we can say that the scientific process has reached that level of development where devices and mechanisms operating on logical principles are successfully created and put into operation.

Another example of the use of logic in modern science is control programs in CNC machines and installations. Here, too, a seemingly iron robot performs logical actions. However, such examples only formally show us the development of modern logic, because such a way of thinking can only be possessed by a living being, such as a person. Moreover, many scientists are still debating whether animals can have logical skills. All research in this area boils down to the fact that the principle of action of animals is based only on their instincts. Only a person can receive information, process it and give the result.

Research in the field of such a science as logic may still go on for thousands of years, because the human brain has not been thoroughly studied. Every year people are born more and more developed, which indicates the ongoing evolution of man.