The laws of logic. General laws of logic

The word "logic" is used by us quite often, but in different meanings. Often people talk about the logic of events, the logic of character, and so on. In these cases, we mean a certain sequence and interdependence of events or actions. “Perhaps he is mad,” says one of the heroes of the story by the English writer G.K. Chesterton, “but there is logic in his madness. There is almost always logic in madness. That's what drives people crazy." Here "logic" just means the presence in the thoughts of a certain general line, from which a person is unable to move away.

The word "logic" is also used in connection with the processes of thought. So, we are talking about logical and illogical thinking, meaning its certainty, consistency, evidence, etc.

In addition, logic is a special science of thinking. It originated in the 4th century. BC, the ancient Greek philosopher Aristotle is considered its founder. Later it became known as formal logic.

In logic, as in any science, the main thing is laws. There are infinitely many logical laws, and this is its difference from most other sciences. Homogeneous laws are combined into logical systems, which are also usually called logics.

Without a logical law, it is impossible to understand what a logical consequence is and what a proof is. Correct, or, as they usually say, logical thinking is thinking according to the laws of logic, according to those abstract patterns that are fixed by them. The laws of logic constitute that invisible frame on which consistent reasoning rests, and without which it turns into chaotic, incoherent speech.

THE CONCEPT OF THE LOGICAL LAW

Before considering the content and specifics of the laws of logic, it is advisable to define the generic concept of "law".

Law is an essential, internal, stable, necessary, recurring connection of phenomena that determines their structure, functioning or development.

Based on this general definition, let's define the category "law of thinking".

The law of thought is an internal, essential, stable, necessary, recurring connection between the elements of thought and the thoughts themselves. The sources of these connections are objective. The laws of thinking are a generalized reflection of the laws of the external world, transformed in the human head and become the general principles of cognitive thinking. Hence, the order and connection of things determines the order and connection of thoughts. This process goes in two directions:

formal (reflection of connections of forms of thought).

The first direction is realized in dialectical laws and studied by dialectical logic, and the second - in formal logical laws and studied by formal logic.

The logical laws express the essential, stable and necessary features of the internal structure of the thought process, which has historically developed on the basis of the objective properties and relations of the natural world. That is why the laws of logic themselves are objective. Therefore, people cannot change or "dictate" new logical laws at their own discretion. The laws of logic are perceived as an axiom - a truth that does not require proof. Possessing the character of universality in the sphere of thinking, these laws are obligatory from the point of view of their observance in all areas of scientific knowledge and at any level of the cognitive process. Naturally, logical laws alone are not enough to ensure the truth of our judgments and conclusions. The laws of logic constitute an important and obligatory moment in the system of conditions that determine the truth of our thoughts. Logical correctness and harmony of thinking are necessary, but not sufficient for the objective truth of inferential knowledge. From this follows the following proposition: the laws of formal logic cannot be absolutized, they do not apply to the external world; their application is limited to the sphere of thinking, and their action is lawful only within the limits of the logical form, and not the content of thought.

It is necessary to pay attention to the fact that although logical laws are relative, they do not act as a mere convention or arbitrary fabrication of the mind. Such laws are the result of the reflection of the external world in the human mind. Only adequately and scientifically comprehended formal logic reveals the objective basis of the logical form of the laws of human thinking and thereby proves their necessity in any process of scientific knowledge of objective reality.

There are the following types of formal-logical laws.

First, laws are associated with individual forms of abstract thinking, or with a concept, or with a judgment, or with a conclusion.

Secondly, laws that are universal in nature operate in all forms of abstract thinking. They are called the basic formal-logical laws. These are the law of identity, the law of contradiction, the law of the excluded middle, and the law of sufficient reason. They are called basic because they:

act in every thought;

underlie various logical operations with concepts and judgments;

used in the process of inference and evidence;

reflect important properties of correct thinking: certainty, logical consistency, consistency, validity.

The first three laws were identified and formulated by the ancient Greek philosopher Aristotle, the law of sufficient reason - by the German philosopher of the 18th century. G.V. Leibniz.

It must be borne in mind that the allocation of four formal-logical laws is carried out only in traditional logic, which is the object of our study. Modern logic (in particular, mathematical, symbolic) has shown that there are infinitely many logical laws and there is no reason to divide them into primary and secondary ones.

In addition, logical systems have been built in which they are not laws, for example, the law of the excluded middle (for example, intuitionistic logic, some systems of many-valued logic), the law of contradiction (paraconsistent logic). However, abstracting from this and remaining within the framework of traditional logic, let us turn to the analysis of the selected formal-logical laws and several more laws (for example, the law of contraposition).

FORMULATION OF LOGICAL LAWS

The law of contradiction.

Of the infinite number of logical laws, the most popular is the law of contradiction. It was discovered one of the first and immediately declared the most important principle not only of human thinking, but of being itself.

At the same time, there has never been a period in the history of logic when this law was not disputed and when discussions around it would completely subside.

The law of contradiction speaks of statements that contradict each other, that is, of such statements, one of which is the negation of the other. These include, for example, the statements “The moon is a satellite of the Earth” and “The moon is not a satellite of the Earth”, “The grass is green” and “It is not true that the grass is green”, etc. In one of the contradictory statements, something is affirmed, in the other, the same thing is denied.

If we denote by the letter A an arbitrary statement, then the expression not-A will be the negation of this statement.

The idea expressed by the law of contradiction seems simple and even banal: a statement and its negation cannot be true together.

Using letters instead of statements, this idea can be conveyed as follows: it is not true that A and not-A. It is not true, for example, that the grass is green and not green, that the Moon is a satellite of the Earth and not a satellite of the Earth, etc.

The law of contradiction speaks of contradictory statements - hence its name. But he denies the contradiction, declares it a mistake, and thereby requires consistency - hence another common name - the law of non-contradiction.

Law of the excluded middle.

The law of the exclusive middle, like the law of contradiction, establishes a connection between statements that contradict each other. And again, the idea expressed by him seems at first simple and obvious: of two contradictory statements, one is true.

In the already used semi-symbolic form: A or not-A, i.e. the proposition A is true or its negation, the proposition not-A, is true.

Specific applications of this law are, for example, statements: “Aristotle died in 322 BC. or he didn't die this year", "Fly maggots have or don't have a head".

The truth of the negation is equivalent to the falsity of the assertion. By virtue of this, the law of the excluded middle can also be expressed in this way: every statement is true or false.

The very name of the law expresses its meaning: things are as described in the statement under consideration, go as its negation says, and there is no third possibility.

The law of identity.

The simplest of all logical laws is perhaps the law of identity. He says: if the statement is true, then it is true, "if A, then A." For example, if the Earth rotates, then it rotates, etc. The pure statement of identity seems so empty of content that it is rarely used by anyone.

The ancient Chinese philosopher Confucius taught his student: "What you know, consider that you know, what you do not know, consider that you do not know." Here it is not just a repetition of the same thing: to know something and to know that you know it are not the same thing.

The law of identity seems extremely simple and obvious. However, it also managed to be misinterpreted. It has been said, for example, that this law states that things always remain unchanged, identical to themselves. This is, of course, a misunderstanding. The law says nothing about mutability or immutability. He only states that if a thing changes, then it changes, and if it remains the same, then it remains the same.

Law of sufficient reason.

The essence of the law: every thought can be recognized as true only when it has a sufficient basis, every thought must be justified. It is written: A is because there is B .

The law of counterposition.

“The law of contraposition” is a general name for a number of logical laws that allow, with the help of negation, to swap the basis and consequence of a conditional statement.

One of these laws, sometimes called the law of simple counterposition, is:

if the first implies the second, then the negation of the second entails the negation of the first.

For example: "If it is true that a number divisible by six is ​​divisible by three, then it is true that a number that is not divisible by three is not divisible by six."

Another law of contraposition says:

if it is true that if not the first, then not the second, then it is true that if the second, then the first.

For example: "If it is true that a manuscript that has not received a positive review is not published, then it is true that a published manuscript has a positive review." Or another example: "If there is no smoke when there is no fire, then if there is fire, there is smoke."

Two more laws of contraposition:

if the case is such that if A, then not-B, then if B, then not-A; for example: "If a square is not a triangle, then the triangle is not a square";

if it is true that if not-A, then B, then if not-B, then A; for example: "If what is not obvious is doubtful, then what is not doubtful is obvious."

CONCLUSION

In terms of content, formal-logical laws are the properties of thought that express the essential features of abstract thinking and underlie all mental operations. In this case, the objective basis of formal-logical laws is the qualitative certainty of objects, their relative stability and mutual conditionality.

BIBLIOGRAPHY

1. Buzuk G.L., Ivin A.A., Panov M.I. The Science of Persuasion: Logic and Rhetoric in Questions and Answers. M., 1992.

2. Grzegorczyk A. Popular logic. M., 1979.

3. Zeget V. Elementary logic. M., 1985.

4. Getmanova A.D. Logic textbook. M., 1994.

5. Ivin A.A. According to the laws of logic. M., 1983.

6. Kirillov V.I., Starchenko A.A. Logics. Textbook. M., 1987.

7. A short dictionary of logic. M., 1991. laws logic. law classical logic statements is a formula that takes ... formula: . As in logic statements in logic predicates, there are generally valid formulas or laws logic. Common formula...

Law Definition

By law in general is meant the internal, essential, necessary connection between objects and phenomena, which is repeated always and everywhere under certain conditions.

Each science studies its specific laws.

So, in physics it is the law of conservation and transformation of energy, the law of universal gravitation. In biology - the law of the unity of the organism and the environment, the law of heredity, etc.

logical law - this is an internal, necessary, essential connection between thoughts, considered from the side of their form.

Compliance with the laws of logic is a necessary condition for achieving truth in the process of reasoning.

Basic formal-logical laws:

1. 1. law of identity;
   2. the law of non-contradiction;
   3. the law of the excluded middle;
   4. the law of sufficient reason.

These laws express certainty, consistency, evidence-based thinking.

They are called basic because they are the most general and define the action. other non-basic laws, which can act as a form of their manifestation:

• • the law of the inverse relation of the volume and content of the concept;
  • the law of distribution of terms in judgment;
  • the law of double negation;
  • laws of construction of inference.

Law of Identity

Any thought in the process of reasoning must have a definite, stable content. This fundamental property of thinking - its certainty - expresses the law of identity.

Identity law:

• any thought in the process of cognition must be identical to itself (a is a, where a is understood as any thought).

Or, every thought in the process of reasoning must be identical to itself:

1. 1. About the same;
   2. The same;
   3. At the same time;
   4. In the same respect.

In other words, the volume and content of thoughts must be clarified and remain unchanged until the end of the argument.

The law of identity can be expressed by the formula:

• • In classical logic: A is A; A = A where A is any thought.
  • In symbolic logic: p → p (if p, then p), where p is any statement, → is the sign of the implication.

Consequences from the law of identity:

1. 1. one cannot identify different thoughts;
   2. identical thoughts cannot be taken for non-identical ones.

The law of identity requires accuracy, clarity, certainty, adequacy, unambiguity from thinking.

Error when violating the law of identity:

The identification of various concepts is a logical error - a substitution of the concept, which can be both unconscious and deliberate.

For example, is it the same thing to say first: “He has a headache”, then - “He has something in his head”, and then - “He is sick all over”? Naturally, in this example, there was a deliberate substitution of the original thought.

Reasons for violating the law of identity:

1. 1. logical - lack of logical culture, undemanding to the accuracy of thought;
   2. linguistic- homonymy of the language (the presence in it of words that are different in meaning, but the same in sound and spelling);
   3. psychological- associativity of thinking.

Violation of these requirements in the process of reasoning is often associated with a different expression of the same thought in the language.

The use of ambiguous words can lead to erroneous identification of different thoughts.

Significance of the law of identity for the work of a lawyer

Compliance with the requirements of the law of identity is important in the work of a lawyer, which requires the use of concepts in their exact meaning. In the trial of any case, it is important to find out the exact meaning of the concepts used by or witnesses, and to use these concepts in a strictly defined sense. Otherwise, the subject of thought will be missed and instead of clarifying the matter, it will be confused.

Law of non-contradiction

Logical thinking is characterized by consistency. Contradictions destroy thought, complicate the process of cognition. The requirement of consistency of thinking expresses the formal-logical law of non-contradiction.

Law of non-contradiction:

• two judgments incompatible with each other cannot be true at the same time; at least one of them is required.

The law is formulated as follows:

• it is not true that A and not-A (two thoughts cannot be true, one of which denies the other).

Two opposing propositions cannot be true at the same time; at least one of them must be false. In other words, if one of the opposite propositions is true, the second one is necessarily false, but they can be false at the same time.

Those. You cannot affirm and deny something at the same time. The law of non-contradiction applies to all incompatible judgments.

The law of non-contradiction is expressed by the formula ():

• • In classical logic: There cannot be both A and not-A, A and B at the same time.
  • In symbolic logic: ┐(р Λ ┐р)(it is not true that p and not-p are both true),

where p is any statement, ┐p is the negation of p, the sign ┐ in front of the whole formula is the negation of two statements connected by a conjunction sign.

Comment

• "A cannot be B and not-B at the same time," or:
• "Of two propositions, of which one affirms what the other denies, one must be false."

The meaning of this law is that nothing can have contradictory qualities at the same time, in the same respect.

For example, we cannot imagine that paper could be both white and non-white, for example, red at the same time. No quality can be both present and absent at the same time.

Thus the law of contradiction requires that we do not attribute contradictory predicates B and not-B to the same thing, at the same time, in the same relation.

More about the law of non-contradiction

To understand it correctly, you need to keep in mind the following:

• in asserting something about any object, one cannot, without contradicting oneself, deny (1) the same thing (2) about the same object, (3) taken at the same time and (4) in the same respect .

The law of contradiction expresses one of the fundamental properties of logical thinking - consistency, consistency of thinking. Its conscious use helps to detect and eliminate contradictions in one's own and other people's reasoning, develops a critical attitude towards all kinds of inaccuracies, inconsistencies in thoughts and actions.

The law of non-contradiction requires consistency in thinking, consistency in reasoning.

Error when violating the law of non-contradiction:

"Inconsistency in Reasoning". In case of an error, the consequence is allowed: (p Λ - p) → q, it reads: if p and not-p, then q, which means: "anything follows from a lie."

Significance of the law of non-contradiction for the work of a lawyer

The ability to reveal and eliminate logical contradictions, often found in the testimony of witnesses, the accused, the victim, plays an important role in judicial and investigative practice.

One of the main requirements for a version in a forensic study is that, when analyzing the totality of factual data on the basis of which it is built, these data do not contradict each other and the version put forward as a whole. The presence of such contradictions should attract the most serious attention of the investigator. However, there are cases when the investigator, having put forward a version that he considers plausible, does not take into account the facts that contradict this version, ignores them, and continues to develop his version in spite of the contradictory facts.

Law of the excluded middle

The law of non-contradiction applies to all incompatible judgments. It establishes that one of them must be false. The question of the second judgment remains open: it may be true, but it may also be false.

The law of the excluded middle applies only in relation to contradictory (contradictor) judgments.

Law of the excluded middle:

• two contradictory propositions cannot be false at the same time, one of them is necessarily true: a is either b or not-b. Either the statement of a fact is true, or its negation.

This is a logical law, according to which either the statement itself is true, or its negation. In other words, one of them is always true, the second is false, the third is not given.

Conflicting (contradictor) judgments

contradictory (contradictory) are called judgments, in one of which something is affirmed (or denied) about each object of a certain set, and in the other it is denied (asserted) about some part of this set. These judgments cannot be both true and false: if one of them is true, then the other is false, and vice versa.

For example, if the proposition “Every Russian Federation is guaranteed to receive qualified legal assistance” is true, then the proposition “Some citizens of the Russian Federation are not guaranteed the right to receive qualified legal assistance” is false. Contradictory are also two judgments about one subject, in one of which something is affirmed, and in the other the same thing is denied. For example: "P. brought to administrative responsibility" and "P. not held administratively liable." One of these judgments is necessarily true, the other is necessarily false.

This law can be written:

• • In classical logic: A or not-A.
  • In symbolic logic, using disjunction:

pV ┐p,

where p is any statement, ┐p is the negation of p.

Like the law of non-contradiction, the law of the excluded middle expresses the consistency, consistency of thinking, does not allow contradictions in thoughts. At the same time, acting only in relation to contradictory judgments, he establishes that two contradictory judgments cannot be not only simultaneously true (as indicated by the law of non-contradiction), but also simultaneously false: if one of them is false, then the other must be true, There is no third.

Of course, the law of the excluded middle cannot indicate which of these judgments is true. This issue is resolved by other means. The significance of the law lies in the fact that it indicates the direction in the search for truth: only two solutions to the problem are possible, and one of them (and only one) is necessarily true.

The law of the excluded middle requires clear, definite answers, pointing to the impossibility of answering the same question in the same sense both “yes” and “no”, to the impossibility of looking for something in between affirming something and denying the same.

The law of the excluded middle requires consistency in thinking, completeness of reasoning.

Error when violating the law of the excluded middle:

"Inconsistency in Reasoning". To bring reasoning to its logical end means to establish which of the contradictory judgments is true and which is false.

Significance of the law of the excluded middle for legal practice

This law is of great importance in legal practice, where a categorical solution of the issue is required. The lawyer must decide the case in the form of "either-or":

• This fact is either established or not established.
• The accused is either guilty or not guilty.

Jus (right) knows only: "either-or".

Law of Sufficient Reason

Our thoughts about any fact, phenomenon, event can be true or false. Expressing a true thought, we must substantiate its truth, i.e. prove its validity. So, when bringing charges against the defendant, the accuser must provide the necessary evidence, substantiate the truth of his assertion. Otherwise, the accusation will be unfounded.

The requirement of proof, validity of thought expresses law of sufficient reason:

• any thought is recognized as true if it has a sufficient basis. If there is b, then there is also its base a.

Any thought is recognized as true if it has a sufficient basis for that.

In other words, in order to accept a thought as true, it is necessary to bring another thought, from which its truth follows.

Doesn't have a symbolic entry., since it allows different forms of justification: sometimes direct perception is enough, sometimes it is necessary to use inference.

The law of sufficient reason requires thinking to be justified, evidence-based, reasoned reasoning.

More

A person's personal experience can be a sufficient basis for thoughts. The truth of some judgments is confirmed by their direct comparison with the facts of reality. So, for a person who witnessed a crime, the justification for the truth of the judgment “N. committed a crime” will be the very fact of the crime of which he was an eyewitness. But personal experience is limited. Therefore, a person in his activities has to rely on the experience of other people, for example, on the testimony of eyewitnesses of an event. Such grounds are usually resorted to in investigative and judicial practice in the investigation of crimes.

Thanks to the development of scientific knowledge, a person is increasingly using the experience of all mankind as the basis of his thoughts, enshrined in the laws and axioms of science, in the principles and provisions that exist in any field of human activity.

The truth of laws, axioms has been confirmed by the practice of mankind and therefore does not need new confirmation. To confirm any particular case, it is not necessary to substantiate it with the help of personal experience. If, for example, we know the law of Archimedes (each body immersed in a liquid loses as much in its weight as the liquid displaced by it weighs), then there is no point in immersing an object in a liquid in order to find out how much it loses in weight. The law of Archimedes will be a sufficient basis for confirming any particular case.

Thanks to science, which in its laws and principles consolidates the socio-historical practice of mankind, in order to substantiate our thoughts, we do not each time resort to checking them, but justify them logically, by deriving from already established provisions.

Thus, any other, already verified and established thought, from which the truth of this thought necessarily follows, can be a sufficient basis for any thought.

If from the truth of judgment A follows the truth of the proposition b, That A will be the basis for b, a b is a consequence of this foundation.

The connection between the foundation and the effect is a reflection in thinking of objective, including cause-and-effect relationships, which are expressed in the fact that one phenomenon (cause) gives rise to another phenomenon (effect). However, this reflection is not direct. In some cases, the logical basis may coincide with the cause of the phenomenon (if, for example, the idea that the number of traffic accidents has increased is justified by pointing to the cause of this phenomenon - ice on the roads). But most often there is no such coincidence. The judgment "It has rained recently" can be substantiated by the judgment "The roofs of the houses are wet"; the footprint of car tire treads is a sufficient basis for the judgment "A car passed at this place." Meanwhile, wet roofs and the trace left by a motor vehicle are not the cause, but the consequence of these phenomena. That's why the logical connection between the basis and the effect must be distinguished from the causal relationship.

More about justification

Validity is the most important property of logical thinking. In all cases when we affirm something, convince others of something, we must prove our judgments, give sufficient reasons confirming the truth of our thoughts. This is the fundamental difference between scientific thinking and non-scientific thinking, which is characterized by lack of evidence, the ability to accept various positions and dogmas on faith. This is especially characteristic of religious thinking, which is based not on proof, but on faith.

The law of sufficient reason is incompatible with various prejudices and superstitions. For example, there are absurd signs: to break a mirror - unfortunately, to sprinkle salt - to a quarrel, etc., although there is no causal relationship between a broken mirror and misfortune, spilled salt and a quarrel. Logic is the enemy of superstition and prejudice. It requires the validity of judgments and is therefore incompatible with statements that are built according to the scheme "after this, therefore, because of this." This logical fallacy occurs when causation is confused with a simple sequence in time, when the antecedent is taken as the cause of the next.

Error when violating the law of sufficient reason:

"Unsubstantiated reasoning", "declarative", "unfounded, unreasoned reasoning". Whenever the question "why?" the answer is "because" there is a violation of the law of sufficient reason.

Significance of the law of sufficient reason for the practice of law

The law of sufficient reason is of great theoretical and practical importance. Fixing attention on the judgments that justify the truth of the put forward provisions, this law helps to separate the true from the false and come to the right conclusion.

The significance of the law of sufficient reason in legal practice is, in particular, as follows. Any conclusion of the court or investigation must be substantiated. In the materials concerning any case, containing, for example, the allegation of the guilt of the accused, there must be data that is a sufficient basis for the accusation. Otherwise, the accusation cannot be recognized as correct. The issuance of a reasoned sentence or court decision in all, without exception, cases is the most important principle of procedural law.

Introduction

Logics is one of the oldest sciences. Its eventful history began in ancient Greece and has two and a half thousand years. At the end of the last - the beginning of this century, a scientific revolution took place in logic, as a result of which the style of reasoning changed radically, methods and science, as it were, gained a second wind. Now logic is one of the most dynamic sciences, a model of rigor and precision even for mathematical theories.

Talking about logic is both easy and difficult at the same time. It is easy because its laws underlie our thinking. Intuitively, they are known to everyone. Any movement of thought that comprehends truth and good is based on these laws and is impossible without them. In this sense, the logic is well known.

One of the heroes of Moliere's comedy only accidentally discovered that he had been speaking prose all his life. So it is with the logic we spontaneously learned. It is possible to constantly apply its laws - and, moreover, very skillfully - and at the same time not have a clear idea of ​​\u200b\u200bit of them.

However, the spontaneously developed skills of logically perfect thinking and the scientific theory of such thinking are completely different things. The logical theory is peculiar. She says about the ordinary - about human thinking - something that seems at first glance unusual and unnecessarily complicated. In addition, its main content is formulated in a special artificial language created especially for these purposes. Hence the difficulty of the first acquaintance with logic: one must look at the familiar and established with new eyes and see the depth behind what seemed self-evident.

Just as the ability to speak existed long before grammar, so the art of thinking correctly existed before the rise of the science of logic. The overwhelming majority of people even now think and reason without turning to special science for help and not counting on this help.

The word "logic" is used quite often, but in different meanings.

Often they talk about the logic of events, the logic of character, and so on. In these cases, we mean a certain sequence and interdependence of events or actions, the presence of a certain common line in them.

The word "logic" is also used in connection with the processes of thought. So, we are talking about logical and illogical thinking, meaning the presence or absence of its properties such as consistency, evidence, etc.

In a third sense, "logic" is the name of a special science of thought, also called formal logic.

It is difficult to find a more multifaceted and complex phenomenon than human thinking. It is studied by many sciences, and logic is one of them. Its subject is logical laws and logical operations of thinking. The principles established by logic are necessary, as are all scientific laws. We may not be aware of them, but we are forced to follow them.

Formal logic is the science of the laws and operations of correct thinking.

The main task of logic is to separate correct ways of reasoning(conclusions, inferences) from wrong.

1. Basic laws of logic

Logical laws form the basis of human thinking. They determine when others logically follow from some statements, and they represent that invisible iron frame on which consistent reasoning rests and without which it turns into chaotic, incoherent speech. Without a logical law, it is impossible to understand what a logical consequence is, and thus what a proof is.

Correct, or, as they usually say, logical thinking is thinking according to the laws of logic, according to those abstract patterns that are fixed by them. This explains the importance of these laws.

Logical laws are objective and do not depend on the consciousness and will of a person. They are not the result of an agreement between people, some special or spontaneous convention. Nor are they the offspring of some "world spirit" or "abstract idea," as some philosophers believed. The power of the laws of logic over a person, their force, which is mandatory for correct thinking, is due to the fact that they are a reflection of the real world, the centuries-old experience of its cognition and transformation by man.

Like all other scientific laws, logical laws are universal and necessary. They act always and everywhere, spreading equally to all people and to any era. The necessity inherent in these laws is in a sense even more urgent and immutable than natural or physical necessity. It is impossible even to imagine that the logically necessary would become different. If something is contrary to the laws of nature and is physically impossible, then no engineer, with all his talent, will be able to realize it. But if something contradicts the laws of logic and is logically impossible, then not only an engineer - even a god could not bring it to life.

There are infinitely many logical laws, but not all of them are equally usable. Some of the simplest and most frequently used of them will be considered below.

2. The law of identity

Outwardly, the simplest of logical laws is the law of identity. He says: if the statement is true, then it is true . In other words, each statement follows from itself and is a necessary and sufficient condition for its truth. Symbolically: A → A If A , That A . For example: “If the house is high, then it is high”, “If the grass is black, then it is black”, etc.

In the applications of the law of identity to specific material, a common feature of all logical laws is revealed with particular clarity. They are tautologies, as if repetitions of the same thing and do not carry meaningful, “subjective” information. These are general schemes, the distinguishing feature of which is that by substituting any specific statements (both true and false) into them, we will definitely get a true expression.

The law of identity is often erroneously replaced by the requirement of stability, certainty of thinking. Indeed, in the process of reasoning, the meanings of concepts and statements should not be changed. They must remain identical to themselves, otherwise the properties of one object will imperceptibly be attributed to a completely different one. If we started talking, for example, about satellites as celestial bodies, then the word "satellite" should, while we are discussing this topic, designate just such bodies, and not some other satellites. The requirement not to change or replace the meanings of words in the course of reasoning is, of course, fair. But, obviously, it is not a law of logic. In the same way, the advice to single out the objects under discussion according to sufficiently stable features does not apply to them in order to reduce the likelihood of substituting one object for another in the reasoning.

Sometimes the law of identity is misinterpreted as one of the laws of being, speaking of its relative stability and certainty. Understood in this way, it turns into the assertion that things always remain unchanged, identical to themselves. Such an understanding of this law is, of course, erroneous. The law says nothing about mutability or immutability. He only asserts that if a thing changes, then it changes, and if it remains the same, then it remains the same.

The first and most important law of logic is the law of identity, which was formulated by Aristotle in the treatise Metaphysics as follows: “... to have more than one meaning means not to have a single meaning; if words do not have (definite) meanings, then all possibility of reasoning with each other, and indeed with oneself, is lost; for it is impossible to think of anything if one does not think (every time) of one thing. One could add to these words of Aristotle the well-known statement that to think (to speak) about everything means not to think (to speak) about nothing.

Law of Identity claims that any thought (any reasoning) must necessarily be equal (identical) to itself, i.e., it must be clear, precise, simple, definite. In other words, this law prohibits confusion and substitution of concepts in reasoning (i.e., using the same word in different meanings or putting the same meaning in different words), creating ambiguity, evading the topic, etc.

For example, the meaning of a seemingly simple statement The students listened to the teacher's explanation incomprehensible, because it violates the law of identity. After all, the word listened to which means that the whole statement can be understood in two ways: either the students listened attentively to the teacher, or they let everyone pass by (and the first meaning is opposite to the second). It turns out that the statement was one, but it has two possible meanings, i.e., the identity is violated: 1 ? 2. In other words, in the above statement, two different (non-identical) situations are mixed (identified).

Similarly, the meaning of the phrase Due to distraction at tournaments, the chess player repeatedly lost points. Without making any comments in this case, it is not clear what is at stake: either the chess player was losing glasses as a device for vision, or as sports scores; two non-identical situations are represented in this statement as identical.

So, due to the violation of the law of identity, such vague statements (judgments) appear.

When the law of identity is violated involuntarily, through ignorance, through inattention or irresponsibility, then simply logical errors arise; but when this law is deliberately violated, in order to confuse the interlocutor and prove to him some false thought, then not just errors appear, but sophisms - outwardly correct proofs of a false thought with the help of a deliberate violation of logical laws. Here is an example of sophism: 3 and 4 are two different numbers, 3 and 4 are 7, so 7 is two different numbers. In this case, as in the above examples, the non-identical is identified: implicitly or gradually they are mixed, equalized, presented as identical, different, unequal, unequal situations (simple enumeration of numbers and addition of numbers), which leads to the appearance of a correct proof of a false thought.

Please note that any sophism, even a very cunning one, is built according to the same scheme - non-identical situations, objects, phenomena, events, ideas, etc. are implicitly identified, which leads to the external plausibility of false reasoning. Therefore, the algorithm for exposing any kind of sophism is quite simple: you just need to find two objects in the argument, which, being non-identical, are imperceptibly identified.

Here is another example of sophism: Which is better: eternal bliss or a sandwich? Of course, eternal bliss. And what could be better than eternal bliss? Of course, nothing! But a sandwich is better than nothing, therefore, it is better than eternal bliss. This example also violates the law of identity.

Not only vague judgments and sophisms are built on violations of the law of identity. They can create all sorts of comic effects. For example, N.V. Gogol in the poem "Dead Souls", describing the landowner Noz-drev, says that he was a "historical person", because wherever he appeared, some kind of "story" was sure to happen to him.

Many funny aphorisms are based on the violation of the law of identity. For example: Do not stand anywhere, otherwise it will fall.

The same principle underlies many anecdotes. For example:

– I broke my arm in two places.

– Don't go to these places again.

Or this joke:

– Do you have quiet rooms in your hotel?

– All our rooms are quiet, but the guests sometimes make noise.

As you can see, in all the examples given, the same technique is used: different meanings, situations, topics are mixed in the same words, one of which is not equal to the other.

Let us cite a few more anecdotes based on violations of the law of identity as examples.

1. - Can you dive?

How long have you been under water?

Until someone pulls it out.

2. - Ah, these childhood dreams. Did any of them come true?

– Yes, I have. As a child, when my mother combed my hair, I dreamed that I would not have hair.

3. Teacher - student:

Why are you late for school today?

- I wanted to go fishing with my father in the morning, but he did not take me with him.

“I hope your father explained to you why you should go to school and not go fishing?”

- Yes, he said that there were few worms and not enough for two.

4. Grandmother tells her grandson about the dangers of smoking, but he objects:

- Here grandfather smokes all his life, and he is already 80 years old!

Grandma retorts:

- And if I didn’t smoke, it would be 90!

5. At the exam, the teacher - student:

- What is your last name?

- Ivanov.

- Why are you smiling?

- I rejoice!

– What exactly?

- The one who answered the first question correctly.

6. When our grandmother was 60 years old, she began to walk 5 kilometers every day. Now she's 80 and we have no idea where she is.

7. Ensign - private:

- I see, comrade soldier, you are too smart!

- Well, not me!

“Sorry, I didn’t know it was yours—it says “common.”

9. Two people meet:

- Peter! Long time no see! How have you changed - beard, mustache, glasses ...

- I'm not Petya!

- Wow! You are no longer Peter!

10. Mother - daughters:

- Daughter, this guy is lame, oblique ... And besides, a complete orphan. You don't have to marry him!

- And I'm not chasing beauty, mom!

- Yes, I'm not talking about that, daughter. The guy had a hard time in his life. Pity the man!

Violation of the law of identity also underlies many of the problems and puzzles known to us since childhood. For example, we ask the interlocutor: “Why (behind what) is there water in a glass?” – deliberately creating ambiguity in this matter ( For what -"for what" and For what - for what subject, where). The interlocutor answers one question, for example, he says: "To drink, water the flowers", and we mean another question and, accordingly, another answer: "Behind the glass."

Let's offer our interlocutor the following problem: "How to divide 12 in such a way that we get 7 without a remainder?"

He will most likely solve it like this: 12: x = 7; x = 12: 7; x =? - and he will say that she does not dare - 12 cannot be divided so that it turns out seven, and even without a trace.

To this, we will object to him that the task is completely solvable: we will represent the number 12 in Roman numerals: XII, and then we will divide this entry with one horizontal line: - ХII-; as you can see, it turned out seven (in Roman numerals) from above and seven from below, and without a trace.

It is clear that this problem is sophistical and is based on the violation of the law of identity, because its mathematical solution is not identical to the graphical one.

At the heart of all tricks is also a violation of the law of identity. The effect of any trick is that the magician does one thing, and the audience thinks completely different, that is, what the magician does is not equal (not identical) to what the audience thinks, which is why it seems that the magician is doing something unusual and mysterious. When opening the focus, we are usually visited by bewilderment and annoyance: it was so simple, how did we not notice it in time.

The famous illusionist Igor Kio demonstrated such a trick. He invited a person from the hall (not a dummy!) and, holding out an open notebook to him, offered to write something there. At the same time, the magician did not see what the guest was writing in the book. Then Kio asked to tear out a page with what was written from the book, return the book to him, and burn the page in an ashtray. After that, the magician, to everyone's surprise, read from the ashes what was written there. Amazed viewers assumed that there was some kind of cunning technique for reading from the ashes or something like that. In fact, everything was much simpler: in the notebook (a page after the one on which the invitee made his entry) there was a carbon paper! And while the audience watched the burning of the torn page, the magician quickly and imperceptibly looked in the book what was written there ...

Here is another trick - intellectual. Think of some number (only not very large, so that it would not be difficult to perform various mathematical operations with it). Now multiply this number by 2 and add 1 to the result. Now multiply what you get by 5. Next, for the resulting number, discard all the digits except the last one, and add 10 to this last digit, then divide the result by 3, add to the resulting number is 2, then multiply the result by 6 and add 50. You get 92.

As a rule, the interlocutor who is offered such a trick is surprised at how you learned the result, because the number he conceived was unknown to you. What actually happens is the following. A person conceived a certain number (for us it is X). Next, you ask him to multiply this number by 2. The result will be even. Then you ask to add 1. The result is bound to be odd. Then the result is multiplied by 5 - and any odd number multiplied by 5 gives a new number that will definitely end in 5 (but not everyone remembers this).

Then you ask the interlocutor to discard all the digits of the resulting number except the last one and then perform various mathematical operations with it. Thus, all further operations are done with the number 5. The trick effect is that your interlocutor does not know about this and it still seems to him that you do not know with what number all actions are performed.

So, the interlocutor thinks (or assumes) one thing, but you do another, and you cannot put an equal sign between the first and second, i.e., the law of identity is violated.

The law of identity manifests itself even in our everyday, actual life. For example, a person makes a promise and fulfills it - in this case, we have a situation of identity (and said and did - what he promised, he fulfilled: one is identical to the other, or 1 = 1 ). It may be that a person does not promise and does not do what he does not promise. This situation is also a manifestation of identity (did not say and did not, did not promise and did not fulfill: one corresponds to, or is equal to, the other, or 0 = 0 ). Finally, there is often a situation where a person promises something to someone and at the same time does not fulfill the promise. In this case, we observe just a violation of the identity (it was said, but it was not done, one is not equal to the other, or 1 ? 0 ). Which of these three situations is the most undesirable? Of course, the last one. When a person promises and fulfills, he acts not only normally, or adequately, but also well. When he does not promise and does not fulfill, he also acts normally and, if not well, then at least honestly, since he does not let anyone down, does not make you hope in vain, count on something, and then be disappointed. When he promises and does not fulfill, he fails not only the other, but also himself, because in this case he “declares” his irresponsibility, disorganization and dishonesty; few people will want to deal with him in the future, and he will have nothing to respect himself for. It is clear that in this case we are not talking about the impossibility of fulfilling this promise due to some unforeseen, sudden and insurmountable circumstances; it means that the person did not fulfill the promise, because he forgot, did not think, did not calculate, relied on “maybe”, etc. As you can see, the violation of identity in the situation under consideration leads to the fact that the violator himself suffers, and those who surround him.

As you can see, the law of identity, its observance and various violations manifest themselves not only in logic, but, by and large, in life itself.

Another of the basic laws of logic is law of contradiction, which says that if one judgment affirms something, and another denies the same thing about the same object, at the same time and in the same respect, then they cannot be true at the same time. For example, two sentences: Socrates is tall And Socrates low(one of them affirms something, and the other denies the same thing, because high is not low, and vice versa) - cannot be simultaneously true if we are talking about the same Socrates, at the same time of his life and in the same respect, i.e., if Socrates is compared in height not with different people at the same time, but with one person. It is clear that when we are talking about two different Socrates or about one Socrates, but at different times of his life, for example, at 10 years old and at 20 years old, or the same Socrates and at the same time of his life is considered in different ways. , for example, he is compared simultaneously with high Plato and low Aristotle, then two opposite judgments may well be true at the same time, and the law of contradiction is not violated.

In other words, the logical law of contradiction forbids asserting something and denying the same thing at the same time. But is it really possible for someone to assert something and then immediately deny the same thing? Will anyone seriously prove, for example, that one and the same person is both tall and short at the same time and in the same respect, or that he is both fat and thin; and blond, and brunette, etc.? Of course not. If the principle of the consistency of thinking is so simple and obvious, then is it worth calling it a logical law and generally paying attention to it?

The thing is, there are contradictions. contact when the same thing is affirmed and immediately denied (the subsequent phrase denies the previous one in the speech, or the subsequent sentence denies the previous one in the text), and distant when there is a significant interval between contradictory judgments in speech or in text. For example, at the beginning of his speech, the lecturer can put forward one idea, and at the end express a thought that contradicts it; it is the same in a book - in one paragraph something can be affirmed that is denied in another. It is clear that contact contradictions, being too noticeable, almost never occur in thinking and speech. The situation is different with distant contradictions: being non-obvious and not very noticeable, they often pass by the visual or mental gaze, are involuntarily skipped, and therefore they can often be found in intellectual and speech practice. So, V. I. Svintsov gives an example from one textbook, in which, with an interval of several pages, it was first stated: “In the first period of his work, Mayakovsky was no different from the futurists,” and then: “Already from the very beginning of his work, Mayakovsky had the qualities which significantly distinguished him from the representatives of futurism.

There are also contradictions explicit And implicit. In the first case, one thought directly contradicts another, and in the second case, the contradiction follows from the context: it is not formulated, but implied.

Explicit contradictions (as well as contact ones) are rare. Implicit contradictions, like distant ones, on the contrary, due to their invisibility, are much more common in thinking and speech.

So, four types of contradictions are obtained: contact and explicit (you can call them differently - explicit and contact, which does not change the essence); contact and implicit; distant and obvious; distant and implicit.

An example of a contact and explicit contradiction is the following statement: Driver N. grossly violated the rules when leaving the parking lot, as he did not take oral permission in writing.

Another example of contact and explicit contradiction: A young girl of advanced years with a short crewcut of dark curly blond hair with a graceful gait of a gymnast, limping, entered the stage.

Such contradictions are so obvious that they can only be used to create some kind of comic effect.

The remaining three groups of contradictions are also comical in themselves, however, being non-obvious and hardly noticeable, they are used quite seriously and create significant communicative interference. Therefore, our task is to be able to recognize and eliminate them.

An example of contact and implicit contradiction: This paper manuscript was created in Ancient Rus' in the 11th century.(in the 11th century there was no paper in Rus' yet).

An example of a distant and obvious contradiction was given above in the form of two statements about V. V. Mayakovsky from one textbook.

Finally, probably, each of us is familiar with the situation when we say to our interlocutor or he tells us: "You contradict yourself." As a rule, in this case we are talking about distant or implicit contradictions, which are quite common in various areas of thinking and life. Therefore, a simple and even primitive at first glance, the principle of consistency of thinking has the status of an important logical law.

It is important to note that there are also contradictions imaginary. A certain mental or speech construction can be constructed in such a way that at first glance it looks contradictory, although in fact it does not contain any contradiction. For example, the well-known statement by A.P. Chekhov seems contradictory When I was a child, I didn't have a childhood for it seems to imply the simultaneous truth of two propositions, one of which denies the other: I had a childhood And I didn't have a childhood. Thus, it can be assumed that the contradiction in this statement is not only present, but is also the most rude - contact and explicit. In fact, there is no contradiction in Chekhov's phrase. Let us recall that the law of contradiction is violated only when it is about the same subject, at the same time and in the same respect. The statement under consideration deals with two different subjects: the term childhood used in various meanings - childhood as a certain age and childhood as a state of mind, a time of happiness and serenity. Although without these comments, most likely, it is quite clear what A.P. Chekhov wanted to say. Let us pay attention to the fact that he used the seeming contradiction, apparently, deliberately, in order to achieve a greater artistic effect. And indeed, thanks to an unreal contradiction, Chekhov's bright and memorable judgment became a successful aphorism.

An imaginary contradiction is often used as an artistic device. It is enough to recall the names of famous literary works: “The Living Corpse” (L. N. Tolstoy), “The Tradesman in the Nobility” (J. Moliere), “The Young Lady-Peasant Woman” (A. S. Pushkin), “Hot Snow” (Yu. V. Bondarev), etc. Sometimes the title of a newspaper or magazine article is built on an imaginary contradiction: “Familiar strangers”, “Ancient novelty”, “Necessary chance”, etc.

Here are some more examples of imaginary contradictions.

I only know that I know nothing(Socrates).

History teaches only that it teaches no one anything.(G. Hegel).

The most incomprehensible thing in the world is that it is comprehensible(A. Einstein).

I hear the silent sound of the divine Hellenic speech(A. S. Pushkin).

So, the law of contradiction forbids the simultaneous truth of two judgments, one of which affirms something, and the other denies the same thing about the same subject, at the same time and in the same respect. However, this law does not prohibit the simultaneous falsity of two such judgments. Remember: Judgments He is tall And He is low cannot be both true if we are talking about the same person, at the same time of his life and in the same respect (relative to some one sample for comparison). However, these judgments may well be simultaneously false under all of the above conditions. If the judgment is true He is of medium height, then judgments He is tall And He is low must be recognized as false. In the same way, judgments can be simultaneously false (but not simultaneously true!) This water is hot And This water is cold; This river is deep. And This river is shallow; This room is bright And This room is dark. We often use the simultaneous falsity of two judgments in everyday life, when, characterizing someone or something, we build stereotypical turns of the type: They are not young, but they are not old either; It's not helpful, but it's not harmful either; He is not rich, but he is not poor either; This thing is not expensive, but not cheap; This act is not bad, but at the same time it cannot be called good.

Judgments are opposite and contradictory. For example, judgments Socrates is tall And Socrates low are opposite, and the judgments Socrates is tall And Socrates low - contradictory. What is the difference between opposing and contradictory judgments? It is easy to see that opposite judgments always presuppose some third, intermediate, intermediate option. For judgments Socrates is tall And Socrates low the third option would be the judgment Socrates of medium height.Conflicting judgments, unlike the opposite, do not allow or automatically exclude such an intermediate option.

No matter how hard we try, we cannot find any third option for judgments. Socrates is tall And Socrates is short(After all, both low and medium height are all low).

It is precisely because of the presence of the third option that opposite judgments can be simultaneously false. If judgment Socrates of medium height - true, then opposite propositions Socrates is tall And Socrates low - false at the same time. In the same way, precisely because of the absence of a third option, contradictory judgments cannot be both false. Such is the difference between opposing and contradictory judgments. The similarity between them lies in the fact that both opposing and contradictory judgments cannot be true at the same time, as required by the law of contradiction. Thus, this law extends both to opposing judgments and to contradictory ones. However, as we remember, the law of contradiction prohibits the simultaneous truth of two propositions, but does not prohibit their simultaneous falsity; and contradictory judgments cannot be simultaneously false, that is, the law of contradiction is insufficient for them and needs some kind of addition.

Therefore, for contradictory judgments, there is law of the excluded middle, which says that two contradictory judgments about the same subject, at the same time and in the same respect, cannot be both true and cannot be simultaneously false (the truth of one of them necessarily means the falsity of the other , and vice versa).

As we can see, the presence in logic of two laws similar to each other (contradiction and the excluded third) is due to the difference between opposing and contradictory judgments.

The law of the excluded middle is played with irony in fiction. The reason for the irony is clear: to say Something is either there or it isn't. means to say absolutely nothing. And it's funny if someone doesn't know this.

In "The tradesman in the nobility" J.-B. Molière has this dialogue:

Mr Jourdain.…And now I must tell you a secret. I am in love with a lady of high society, and I would like you to help her write a little note, which I am going to drop at her feet.

Philosophy teacher. Surely you want to write poetry for her?

Mr Jourdain. No, no, not poetry.

Philosophy teacher. Do you prefer prose?

Mr Jourdain. No, I don't want prose or poetry.

Philosophy teacher. You can't do that: it's either one or the other.

Mr Jourdain. Why?

Philosophy teacher. For the reason, sir, that we can express our thoughts in no other way than prose or verse.

Mr. Jourdin. Not otherwise than prose or poetry?

Philosophy teacher. Not otherwise, sir. Everything that is not prose is poetry, and everything that is not poetry is prose.

One of the basic laws of logic, along with the laws of identity, contradiction, and the excluded middle, is law of sufficient reason, which claims that any thought (thesis), in order to be valid, must necessarily be proved (justified) by some arguments (grounds), and these arguments must be sufficient to prove the original thought, i.e. it must follow of them with necessity (the thesis must necessarily follow from the grounds).

Let's give some examples. In reasoning This substance is electrically conductive(thesis), because it is metal(base) the law of sufficient reason is not violated, since in this case the thesis follows from the base (from the fact that the substance is a metal, it follows that it is electrically conductive). And in the discussion Today the runway is covered with ice(thesis), because planes can't take off today(ground) the law in question is violated, the thesis does not follow from the ground (because the planes cannot take off, it does not follow that the runway is covered with ice, because the planes may not take off for another reason). The law of sufficient reason is also violated in a situation where a student says to the teacher at the exam: Don't give me a deuce, ask again(thesis), I've read the whole tutorial, maybe I'll answer something(base). In this case, the thesis does not follow from the foundation (the student could read the entire textbook, but this does not mean that he will be able to answer something, since he could forget everything he read or understand nothing in it, etc.).

In reasoning The crime was committed by N.(thesis), After all, he himself admitted this and signed all the testimony(reason) The law of sufficient reason is, of course, violated, because the fact that a person confessed to a crime does not follow that he actually committed it. As you know, you can confess to anything under the pressure of various circumstances (whatever people did not “confess” in the dungeons of the medieval Inquisition and the offices of repressive authorities, they easily “confess” to anything on the pages of the tabloid press, in various television talk shows and so on.). Thus, the important legal principle of the presumption of innocence is based on the law of sufficient reason, which prescribes that a person be considered innocent, even if he testifies against himself, until his guilt is proven.

Let us give examples of small arguments in which the law of sufficient reason is violated.

This person is not sick, because he does not have a fever.

In one American state, a flying saucer crashed, because it was written about in newspapers, it was broadcast on the radio and even shown on television.

« ... You are to blame for the fact that I want to eat"(I. A. Krylov" The Wolf and the Lamb ").

Water extinguishes fire because it is liquid and cold.

The law of sufficient reason, requiring probative force from any reasoning, warns us against hasty conclusions, allegations, cheap sensations, hoaxes, rumors, gossip and fables. Pay attention to such proverbs that you probably know, such as: Trust, verify; Don't believe your eyes; Don't believe your ears; They say that chickens are milked; Tongue without bones and many others, are a kind of consequences (or manifestations) at the level of intuitive logic of the law of sufficient reason. By prohibiting taking anything on faith, the law of sufficient reason acts as a reliable barrier to any intellectual fraud. It is no coincidence that it is one of the main principles of science (as opposed to pseudoscience, or pseudoscience).

Science throughout its history was accompanied by pseudoscience (alchemy, astrology, physiognomy, numerology, etc.). Moreover, pseudoscience, as a rule, disguises itself as science and hides behind its well-deserved authority. Therefore, science has developed two reliable criteria (principle) by which one can distinguish scientific knowledge from pseudoscientific. The first criterion is the principle verification(lat. Veritas-"true", facere-“do”), which prescribes to regard as scientific only that knowledge that can be confirmed (one way or another, directly or indirectly, sooner or later). This principle was proposed by the famous English philosopher and scientist of the 20th century, Bertrand Russell. However, sometimes pseudosciences build their arguments so skillfully that everything they say seems to be confirmed. Therefore, the principle of verification is supplemented by the second criterion, which was proposed by the great German philosopher of the 20th century, Karl Popper. This is the principle of falsification (lat. false -"lie", facere-“do”), according to which only that knowledge can be considered scientific, which can (one way or another, directly or indirectly, sooner or later) be refuted. At first glance, the principle of falsification sounds strange: it is clear that scientific knowledge can be confirmed, but how to understand the statement by which it can be refuted. The fact is that science is constantly developing, moving forward: old scientific theories and hypotheses are being replaced by new ones, refuted by them; Therefore, in science, not only the verifiability of theories and hypotheses is important, but also their refutation. For example, from the point of view of ancient science, the center of the world is the Earth, and the Sun, Moon and stars move around it. It was precisely the scientific idea that existed for about two thousand years: within its framework, observations were made, discoveries were made, maps of the starry sky were compiled, and the trajectories of celestial bodies were calculated. However, over time, this idea became outdated: the accumulated facts began to contradict it, and in the 15th century a new explanation of the world structure appeared, according to which the Sun is at the center of the Universe, and the Earth, along with other celestial bodies, moves around it. Such an explanation, of course, refuted the ancient idea of ​​the Earth as the center of the world, but from this it did not cease to be scientific at all, but, on the contrary, remained so - only for its time.

If the principle of verification, taken separately, pseudoscience can bypass, then against the two principles together (verification and falsification), it is powerless. A representative of pseudoscience, of course, can say: "In my science, everything is confirmed." But will he be able to say: "My ideas and statements will ever be refuted and give way to new, more correct ideas"? That's the thing, it can't. Instead, he will say something like this: "My science is ancient, thousand years old, it has absorbed the wisdom of the ages, and nothing in it is subject to refutation." When he claims that his ideas are irrefutable, he thereby, on the principle of falsification, declares them to be pseudoscientific. In contrast, the representative of science, the scientist, recognizes both the verifiability at the present moment and the future refutability of his ideas. “My statements,” he will say, “are now being confirmed in such and such a way, but time will pass, and they will give way to new ideas, more solid and more true.”

Pseudoscience cannot circumvent the principle of falsification, because, unlike science, it does not develop, but stands still. Let us compare the results of the development of various sciences with the achievements of pseudosciences: sciences have achieved tremendous success in their history (from a stone ax to a modern computer, from animal skins and cave life to the exploration of interstellar space), and various pseudosciences remain today at the same level as at the dawn of human history (modern astrologers, numerologists, ufologists, parapsychologists, psychics and healers tell a person about the same thing as ancient shamans, magicians and sorcerers).

If some kind of knowledge can neither be confirmed (verified) nor refuted (falsified), then it is pseudo-scientific, pseudo-scientific, pseudo-scientific, para-scientific, i.e., non-scientific.

So, we have considered the four basic laws of logic. Now let's give some examples of different situations in which they are violated.

1. - Why do you call this choir mixed? After all, there are only women.

Yes, but some people can sing and others can't.

(The law of identity is violated).

2. - Do you like her?

– Hardly: I can’t say that I like her.

Well, then you don't like her!

– No, this is also wrong: I can’t say that I don’t like her.

So, do you like it or not? How to understand you?

Yes, I don't understand myself...

3. Babin took the pipe out of his mouth. Laughing with his eyes, he asked:

“Wait, Makletsov, have you read Les?”

“I didn’t read a single book during the war,” Makletsov said with dignity.

“Well, you were supposed to have read this before the war.

- And if it was supposed to, then I read it.

(Violated the law of sufficient reason)

4. - All the same: did you read it or not?

- Why are you piled on, comrade battalion commander, you fetter any initiative! Forest. In the forty-first, surrounded in such forests, I fought, which Ostrovsky never dreamed of ...

(The law of identity is violated).

(G. Baklanov« Military stories»).

5. A peasant came to the sage and said: "I argued with my neighbor." He outlined the essence of the dispute and asked: "Who is right?" The sage replied: "You are right." After some time, the second of those arguing came to the sage. He also spoke about the dispute and asked: “Who is right?” The sage replied: "You are right."

6. “How so? one of the friends accompanying him asked the sage, “it turns out that the first is right, and the second is right?” The wise man answered him: "And you are right too."

(Violated the law of the excluded middle).

7. Wanting to know if the air has weight, Aristotle blew a bull bladder with it and weighed it. Then he let the air out of it and weighed it again. The weight was the same in both cases. From this, the philosopher concluded that air is weightless.

8. Alice meets the White King. He says:

- Look at the road! Who do you see there?

“No one,” said Alice.

- I would like such a vision! said the King with envy. - See Nobody! Yes, even at such a distance! (The law of identity is violated).

(L. Carroll« Alice in the Wonderland»)

(Violation of the law of sufficient reason).

9. A girl with full buckets is good; empty buckets - for worse.

(Violation of the law of sufficient reason).

10. The student asks the teacher:

Is it possible to scold or punish a person for what he did not do?

“Of course not,” the teacher replies.

“In that case, don’t scold or punish me,” the student says, “I didn’t do my homework today…

(The law of identity is violated).

11. - Great! Rudin said. “So, in your opinion, there are no convictions?”

- No, it doesn't exist.

- Is that your belief?

How do you say they don't exist? Here's one for you, for the first time.

(The law of contradiction is violated).

(I. S. Turgenev« Rudin»)

12. In 1907, the Cadet faction in the State Duma, on the question of attitude towards the government, decided: not to express either confidence or distrust in him; moreover, if a resolution of confidence in the government is introduced, then vote against it, and if a resolution of no confidence in the government is introduced, then vote against it.

(Violated the law of the excluded middle).

13. One comrade said to another:

Buy a hundred oranges, I'll eat one.

- Don't eat!

- Let's argue.

They argued, one of them bought a hundred oranges, and the other took one orange and ate it.

– And the rest? - the one who bought the oranges was indignant.

– What are the others? another asked incredulously.

- Eat the rest!

“For what reason?” I said: I'll eat one, so I ate it.

(The law of identity is violated).

14. Father Cristoforo was very smart.

“Tell me, Reverend Father,” I once asked… “To all appearances, the teachings of Christ failed to turn a person into an angel in almost two millennia!..

- Smart you asked me a question ... Yes, it's true! But I'll tell you something else. Look at you. Water has existed in the world for perhaps several million years, and you still have a dirty neck! And he pointed his finger at me.

I was dumbfounded when I heard such a simple truth...

(The law of identity is violated).

(G. Morcinek« Seven amazing stories of Joachim Rybka»)

We walked along Neglinnaya,
We went to the boulevard
They bought us blue-blue,
Pretty red ball.

(The law of contradiction is violated).

(WITH. V. Mikhalkov)

16. In the very sun, returning home, Nasreddin asked his wife:

- Bring me a bowl of curdled milk, there is nothing more useful and pleasant for the stomach in this heat! The wife replied:

- Yes, we don’t just have bowls, we don’t even have a spoonful of yogurt in the house!

Nasreddin said:

- Well, it’s good that it’s not, because yogurt is harmful to humans.

(The law of contradiction is violated).

17. The wife was surprised:

- You are a strange person - at first he said that yogurt is useful, then he immediately said that it was harmful.

- What is strange here, - answered Nasreddin, - if it is in the house, then it is useful, and if it is not in the house, then it is harmful.

(Violation of the law of sufficient reason).

18. – Do we know the world?

We probably know.

- That's for sure?

– I don’t know… It is possible that he is unknowable.

- So, maybe then the statement that the world is unknowable is more correct?

– I don’t know… It’s also possible that it is cognizable.

- So all the same - do we know the world or not?

- Who knows? It can be both knowable and unknowable at the same time.

(Violated the law of the excluded middle).