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The first law of logic is the law of identity. Open Library is an open library of educational information. In everyday life

Introduction

In addition to the laws of materialistic dialectics, human thinking is also subject to the laws of logic. These are the basic laws of logic: the law of identity, the law of non-contradiction, the law of the excluded middle, the law of sufficient reason, etc. They are used in operating concepts and judgments, used in inferences, proofs and refutations.

The first three were discovered by Aristotle, the fourth - by V.G. Leibniz. Logical laws reflect in a person's consciousness certain relations that exist between objects, or reflect such ordinary properties of objects as their relative stability, certainty, incompatibility in the same object of the simultaneous presence and absence of the same signs.

The laws of logic reflect the objective in the subjective consciousness of a person, therefore they cannot be canceled or replaced by others. are of a common human nature, since they are the same for people of all races, nations, professions. The basic logical laws have developed historically as a result of centuries of practice of knowledge. They reflect such important properties of correct thinking as its certainty, consistency, validity, clarity of thinking, choice "either-or" in certain "tough" situations. In addition to the basic ones, there are many non-basic laws of logic that must be fulfilled when operating with concepts, or judgments, or inferences.

Identity law.

The first and most important law of logic is the law of identity, which was formulated by Aristotle in his treatise "Metaphysics" as follows: to reason with each other, but in reality - with oneself; for it is impossible to think anything if you do not think one thing. " One could add to these words of Aristotle the well-known statement that thinking (talking) about everything means not thinking (not talking) about anything.

The law of identity states that any thought (any reasoning) must necessarily be equal (identical) to itself, that is, it must be clear, precise, simple, definite. In other words, this law prohibits confusing and substituting concepts in reasoning (that is, using the same word in different meanings or putting the same meaning in different words), creating ambiguity, deviating from the topic, etc. For example, the meaning of the phrase is not clear: "Due to absent-mindedness at tournaments, a chess player has repeatedly lost points." Obviously, due to violation of the law of identity, vague statements (judgments) appear. The symbolic record of this law looks like this: a> a (read: "If a, then a"), where a is any concept, statement or whole reasoning.

When the law of identity is violated involuntarily, out of ignorance, then there are simply logical errors; but when this law is violated deliberately, in order to confuse the interlocutor and prove to him some false thought, then not only errors appear, but sophisms. Thus, sophism is an outwardly correct proof of a false thought with the help of a deliberate violation of logical laws.

However, not only vague judgments and sophisms are built on violations of the law of identity. By breaking this law, you can create some kind of comic effect. For example, Nikolai Bacilievich Gogol in the poem "Dead Souls", describing the landowner Nozdrev, says that he was a "historical person", because wherever he appeared, some kind of "story" always happened to him. Many comic aphorisms are based on the violation of the law of identity. For example: "Do not stand anywhere, otherwise it will get in."

Violation of this law is also at the heart of many of the problems and puzzles we have known since childhood. For example, we ask the interlocutor: "What (why) is the water in a glass glass for?" - deliberately creating ambiguity on this issue (why - for what and for what - for what subject, where). The interlocutor answers one question, for example, he says: "To drink, water the flowers", but we mean another question and, accordingly, another answer: "Behind the glass."

All tricks are also based on violation of the law of identity. The effect of any focus is that the magician does one thing, and the audience thinks completely differently, 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, as a rule, we are visited by bewilderment and annoyance: it was so simple, how could we not notice it in time.

The law of identity was formulated by Aristotle in his 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 in reality - with oneself is lost; for it is impossible to think of anything if you do not think (each time) of one thing "

Application

In everyday life

Any of our acquaintances changes every year, but we still distinguish him from other familiar and unfamiliar people (there is a possibility of distinction), because he retains the basic features that appear as the same throughout the life of our friend (there is a possibility of identification ). That is, in accordance with Leibniz's law(defining the concept of identity) we claim that our friend has changed. However, according to the law of identity we claim that this is one and the same person, since the definition is based on the concept of personality. The law of identity requires that we always use the same expression (name) to describe the same concept. Thus, we simultaneously consider one object (familiar) at two different levels of abstraction. The possibility of discrimination and identification is determined in accordance with the law of sufficient reason. In this case, our sensory perception is used as a sufficient basis (see identification).

A growing tree does not cease to be a tree, although it is in a state of continuous change and development.

This relative stability, the certainty of objects of reality is displayed in our consciousness in the form of the law of identity, which expresses the certainty of our thoughts and their constancy in the process of this reasoning.

Just as in nature and in society, objects and phenomena do not mix with each other, but have their own specific, definite features, so our thoughts about objects and phenomena should not be mixed with each other.

Correctly arguing about any phenomenon of reality, in our thoughts we do not replace the studied subject with another subject, do not mix different concepts, do not allow ambiguity. Accuracy and definiteness of thinking is the law of correct thinking.

In jurisprudence

Compliance with the requirements of the law of identity is of great importance in the work of a lawyer. For example, in investigative practice, they often resort to identification, that is, to establish the identity of a person or object by signs and characteristics by presenting them to a witness, victim, suspect or accused. The essence of this investigative action, based on the law of identity, consists in establishing the fact that an object perceived in one setting is the same object perceived in another setting.

In formal logic

Under the identity of a thought to itself, in formal logic, we understand the identity of its volume. This means that instead of a logical variable, thoughts of different concrete content can be substituted into the formula “is” if they have the same volume. Instead of the first in the formula "is", we can substitute the concept "animal; with a soft earlobe ", and instead of the second - the concept "Animal capable of producing tools"(both of these thoughts from the point of view of formal logic are considered equivalent, indistinguishable, since they have the same volume, namely, the signs reflected in these concepts refer only to the class of people), and thus a true judgment is obtained "An animal with a soft earlobe is an animal with the ability to produce tools.".

In mathematics

Here the concept of arithmetic equality of numbers is considered as a special case of the general concept of logical identity. However, there are mathematicians who, in contrast to this point of view, do not identify the symbol "", which occurs in arithmetic, with the symbol of logical identity; they do not believe that equal numbers are necessarily identical, and therefore consider the concept of numerical equality as a specifically arithmetic concept. That is, it is believed that the very fact of the presence or absence of a special case of logical identity should be determined within the framework of logic. ...

Violations of the law of identity

When the law of identity is violated involuntarily, out of ignorance, then logical errors arise, which are called paralogisms; but when this law is deliberately violated, in order to confuse the interlocutor and prove to him some false thought, then errors appear, called sophisms.

If the law of identity is violated, the following errors are possible:

Amphibolia(from the Greek. ἀμφιβολία - ambiguity, ambiguity) is a logical error, which is based on the ambiguity of linguistic expressions. For instance: "They say correctly that the language will bring you to Kiev. I bought a smoked tongue yesterday. Now I can safely go to Kiev." Another name for this error is "thesis substitution".
Equivocation(from lat. aequivocatio- equal voice, ambiguity) is a logical error in reasoning, which is based on the use of the same word in different meanings. For example, the meaning of a seemingly simple statement: "Students listened to the teacher's explanation", - is incomprehensible. After all, the word "listened", which means that the whole statement can be understood in two ways: either the students listened attentively to the teacher, or they ignored everything (the first meaning is opposite to the second). Equivocation is sometimes used as a rhetorical artistic device. In logic, this technique is called "concept substitution."
Logomachia(from the Greek. λόγος - word and μάχη - fight, battle) dispute about words, when during the discussion the participants cannot come to a common point of view due to the fact that they did not clarify the initial concepts.

Masters of deliberately incorrect reasoning, calculated to mislead their interlocutor, were, for example, the ancient Greek sophists (hence the word and "sophism"). As a rule, the sophists used in their reasoning such concepts that had different meanings. For example, let's take a look at the "horned" sophism:

What you have not lost, you have.

You haven't lost your horns.

Therefore, you have horns.

The trick of the sophists in this case is based on the fact that the word "lost" is interpreted ambiguously. In the first line, the words "did not lose" refer to those items that we have and which we did not lose, and in the second, the words "did not lose" refer to those items that we never had. It is clear that the conclusion cannot be correct.

However, not only vague judgments and sophisms are built on violations of the law of identity. By breaking this law, you can create some kind of comic effect. For example, Nikolai Vasilyevich Gogol in the poem "Dead Souls", describing the landowner Nozdrev, says that he was a "historical person", because wherever he appeared, some kind of "story" always happened to him. Many comic aphorisms are based on the violation of the law of identity. For instance: "Do not stand anywhere, otherwise it will fall." Also, many anecdotes are created by violating this law. For instance:

- I broke my arm in two places.

“Don't go to these places anymore.

Or such an anecdote:

- Do you have quiet rooms in the hotel?

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

Notes (edit)

Literature

Kirillov V.I. Starchenko A.A. Logics. - M .: Higher school, 1982 .-- 264 p. - 100,000 copies
Aristotle. Metaphysics // Anthology of world philosophy in four volumes. - M .: Mysl, 1969 .-- T. 1. - 936 p. - 35,000 copies.
Gusev D.A. A short course in logic. - M .: NTs ENAS, 2003 .-- 190 p. - ISBN 5-93196-357-X
Philosophical Dictionary / Ed. I.T.Frolov .. - 4th ed. - M .: Politizdat, 1981 .-- 445 p. - 700,000 copies
Boyko A.P. Logics. - M .: New school, 1994 .-- 80 p. - 50,000 copies. - ISBN 5-7301-0053-1
Vinogradov S. N. Kuzmin A. F. Logics. - eighth edition. - M .: Uchpedgiz RSFSR, 1958 .-- 176 p. - 800,000 copies
A. An introduction to the logic and methodology of the deductive sciences. - M.: Ed. Inost. Literature, 1948 .-- 326 p.
Gorsky D.P. Tavanets P.V. Logics. - M .: Politizdat, 1956 .-- 280 p. - 75,000 copies

Examples of violation of the laws of logic

Law of sufficient reason

It is formulated as follows: "Any thought, in order to become reliable, must be substantiated by other thoughts, the truth of which is proven or obvious."

This law requires that our judgments about the subject and its properties should not be unfounded, but logically follow from reliable facts and arguments, ᴛ.ᴇ. requires evidence of thinking. Judgments that are made to substantiate the truth of another judgment are called a logical basis. A judgment arising from a logical foundation is usually called a logical consequence. The basis is the laws and axioms of science, statistical data, objective experience of social development, etc. An example of sound reasoning might be: “This substance is electrically conductive (consequence), since it is metal (base)". The law of sufficient reason is not violated, since a consequence follows from the base with extremely important (from the fact that the substance is a metal, it follows with extreme importance that it is electrically conductive, since the electrical conductivity of metals has been proven by science).

An important legal principle is based on this law - the presumption of innocence.

On violation identity law false alibis are based, false or erroneous testimony of witnesses or the defendant in court, an indication of a false trail, etc. Quite often, violation of the law of identity is used in journalism. For example, on the first page of a newspaper you read an intriguing headline (announcement) like “At last a perpetual motion machine has been created!” or "There is a dog in California that predicts the future." At the same time, having bought the issue and read the article, you are convinced that its content does not entirely correspond to the title.

You can give such an example of substitution of concepts (different meanings embedded in the same words): “The teacher to the student:“ I hope I don’t see what you are cheating. ” Pupil to teacher: “I also hope so ...”. An example when different non-identical situations are identified: Judge to the victim: “You claim that the accused called you a fool. It's true?" "The truth is, Mr. Judge." "Then what are you complaining about?"

A classic example of violation the law of contradiction is a quote from the work of I.S. Turgenev "Rudin":

"Wonderful!" - said Rudin. - So, in your opinion, there are no convictions?

"It does not and does not exist."

"Is this your belief?"

“How do you say that they are not there? Here's one for you, for the first time. "

Examples of violations excluded third law there may be recognition as true or false at the same time of such judgments: “All businessmen of the city are honest” and “Some businessmen of the city are not honest”, “Mariupol is a settlement” and “Mariupol is not a settlement”.

An example of a violation law of sufficient reason the following statements can be considered: “The crime was committed by N., since he himself admitted it and signed all the testimony with his own hand”, “Student Ivanov should be given a test in physics, since he is leaving for the competition.” Another example: a student says to the teacher during the exam: “Don’t give me a bad, ask something else, I read the textbook, maybe I will answer something”.

This law reveals the essence of the requirement for the certainty and unambiguity of our thoughts. The law of identity can be formulated as follows: the volume and content of thought about an object must be strictly defined and remain constant in the process of reasoning about it.

It is customary to express the law of identity by the formula A = A or A essence A.

In accordance with the law of identity, when arguing about something, we must clarify the scope and content of the concepts we use and, in the process of reasoning and inference, strictly adhere to the constraints (parameters) chosen by us at the beginning, without replacing them with others in the course of reasoning. The fulfillment of this requirement guarantees us the accuracy, certainty, unambiguousness of our reasoning; creates an opportunity to distinguish and identify objects in formal systems in terms of expressing them. A conscious limitation of the volume and content of thoughts about various objects allows, on the basis of the law of identity, to produce an abstraction of their identification. In other words, the law of identity is reduced to the fundamental uniqueness of the concepts used by us throughout the entire reasoning and conclusion.
Let's pay attention to the fact that the concept of the identity of things, phenomena, processes, ideas, etc. there is idealization, which is obtained as a result of abstraction from the properties and aspects of the subject of reasoning that are not essential at the moment. In order to carry out a logical operation, we must reduce the judgment to one of two logical values: either true or false. This is done when specifying the scope and content of the concepts used.

The law of identity is valid only in the thought process; it does not apply to material relations of the objective world, i.e. is not an absolute law of reality. Therefore, to talk about its observance means to insist on the discipline of our thinking, i.e. on the mandatory nature of correct thinking, without which it is impossible to obtain true knowledge. Violation of the law of identity leads to a logical error, which can be characterized as the loss or substitution of the object of thought. It can occur either involuntarily or intentionally. The first case (involuntarily) may be the result of a low culture of mind, inability to correctly use existing knowledge, lack of skills in systemic thinking, etc., as well as inability to control their emotions during reasoning or proof (discussion, argument, etc.); the second case (deliberate distortion of the subject of thought in the concept) is most often set by ideological or narrowly practical considerations and is addressed to a low-culture audience, which we can record during election campaigns. Unfortunately, the arrival of new people in politics is not necessarily accompanied by an increase in their logical culture. In addition, it must be borne in mind that the meaning of the concepts that we use in proof and inference is determined by the context; seemingly similar concepts can have different content depending on the context. For example, the concept of "democrat" can mean "supporter of liberal ideas", "fighter for human rights", etc., or maybe just "a member of the Democratic Party." From the point of view of formal logic, the concept of "democrat" should be considered vague, and for this reason it must be clarified, otherwise the law of identity will not be observed. In the course of reasoning, we must adhere to the meaning of this concept that we introduced at the very beginning.

From the above reasoning, it is clear that the observance of the law of identity is largely determined by our ability to use concepts. In the course of reasoning (written or oral), it becomes necessary for the purposes of stylistic diversity to express the same concepts in different words, but in this case it is necessary to ensure that the newly introduced words as concepts would be identical to the already introduced concepts, commensurate with them. For example: “In support of the provisions put forward, the candidate gave convincing arguments. His arguments were accepted by the audience with approval. " Here the concepts of "arguments" and "arguments" coincide, i.e. are identical. In another example on the same topic: “In support of the provisions put forward, the candidate gave convincing arguments. His speech was greeted with thunderous applause "- we compare the concepts of" arguments "and" speech ". Obviously, they are not identical, because “speech” includes not only arguments, but also stylistics, intonation, gestures, logic, etc., while “arguments” as concepts indicate the theoretical and logical sides. Obviously, the law of identity is not observed here, which is why the description of the event has the character of indefiniteness, vagueness, and understatement.

Another example: “Everything flows; you cannot enter the same river twice ”(Heraclitus). In one of the Kharkov newspapers we read the headline: "The wise man said:" You cannot enter the same water twice. " If we compare the concepts of "river" and "water", then it is clear that they are not identical, because water can be stagnant (in a basin, in a swamp, in a pond, etc.), and the river is always in motion. The one who placed this title violated the law of identity and thereby distorted the most important provision of the Heraclitean doctrine of dialectics, which reveals the essence of movement. If you read the texts carefully, you yourself can find examples of both positive and negative nature.

The law of identity- the principle of constancy or the principle of preservation of the objective and semantic meanings of judgments (statements) in some obviously known or implied context (in the conclusion, proof, theory). It is one of the laws of classical logic.

In the process of reasoning, each concept, judgment should be used in the same sense. A prerequisite for this is the possibility of distinguishing and identifying those objects in question. ... A thought about an object should have a definite, stable content, no matter how many times it is repeated. The most important property of thinking is its certainty- is expressed by this logical law.

Application

In everyday life

In jurisprudence

In formal logic

In formal logic, the identity of thought to itself is understood as the identity of its volume. This means that instead of a boolean variable A (\ displaystyle A) into the formula " A (\ displaystyle A) there is A (\ displaystyle A)»Thoughts of different concrete content can be substituted if they have the same volume. Instead of the first A (\ displaystyle A) in the formula " A (\ displaystyle A) there is A (\ displaystyle A)»We can substitute the concept "animal; with a soft earlobe ", and instead of the second - the concept "Animal capable of producing tools"(both of these thoughts from the point of view of formal logic are considered equivalent, indistinguishable, since they have the same volume, namely, the signs reflected in these concepts refer only to the class of people), and thus a true judgment is obtained "An animal with a soft earlobe is an animal with the ability to produce tools.".

In mathematics

In mathematical logic, the law of identity is the identically true implication of a logical variable with itself X ⇒ X (\ displaystyle X \ Rightarrow X) .

In algebra, the concept of arithmetic equality of numbers is considered a special case of the general concept of logical identity. However, there are mathematicians who, contrary to this point of view, do not identify the symbol " = (\ displaystyle =)», Found in arithmetic, with the symbol of logical identity; they do not believe that equal numbers are necessarily identical, and therefore consider the concept of numerical equality as a specifically arithmetic concept. That is, it is believed that the very fact of the presence or absence of a special case of logical identity should be determined within the framework of logic. ...