Features of modern logic. Logical thinking - the development of logic The place of logic in the system of scientific knowledge

Moscow state academy utilities and construction

(name of the department)

________________________________________________________________

(surname, name, patronymic of the student)

Faculty ______________ course ____________ group _____________

TEST

By discipline _________________________________________________

On the topic __________________________________________________

(topic name) ________________________________________________________________

Mark of offset _________________________ __________

(pass/fail) (date)

Supervisor __________________________________ __________________

(full name, position, academic degree, academic title) (signature)

Moscow 20__

TEXTS OF LECTURES

TO THE COURSE OF THE EDUCATIONAL DISCIPLINE "LOGIC"

Topic 1. SUBJECT AND SIGNIFICANCE OF LOGIC

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

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

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

Philosophy- studies the relationship between matter and thought.

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

Cybernetics- studies thinking as an information process.

Psychology- studies the mechanisms for the implementation of mental acts, including brain ones, and understands thinking as a cognitive activity.

The role of thinking in cognition.

A person from the first days of his life is included in the process of cognition of the world around him. He recognizes individual signs of objects and phenomena that are reflected in sensations. ; holistic objects and phenomena in their immediate givenness to a person are presented in perception ; visible and invisible to the human eye connections and relationships between objects and phenomena allows you to open thinking . In a broad sense, a person's thinking is understood as his active cognitive activity with an internal process of planning and regulating external activities. To understand how a person thinks means to understand how he sees (represents, reflects) the world around him, himself in this world and his place in it, and also how he uses knowledge about the world and about himself to control his own behavior.

Cognition is the construction of the semantic (ideal) content of the world in the minds of people. The world and its properties are revealed in the process of cognition. Practice is one of the elements of knowledge. In practical activities, people encounter various properties of objects and phenomena. Knowledge has two main stages: sensual And rational.

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

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

Any empirical knowledge begins with living contemplation, sensory perceptions. Forms sensory perception are reflections of individual properties of objects or phenomena that directly affect the senses. Each item has not one, but many properties. Feelings reflect various properties of objects.

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

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

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

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

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

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

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

Distinguish inferences inductive, deductive And Similarly.

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

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

1.3. The main stages in the development of logic

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

History shows that individual logical problems arise before the mind's eye of man already over 2.5 thousand years ago - first in ancient India and ancient China. Then they get a more complete development in ancient Greece and Rome. Only gradually do they develop into a more or less coherent system, taking shape as an independent science.

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

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

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

A significant contribution to the development of logic was made by medieval scholastics. The Latin terminology introduced by them is still preserved.

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

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

Inductive logic was later systematized and developed English philosopher and scientists John Stuart Mill(1806-1873) in his two-volume work "The System of Syllogistic and Inductive Logic".

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

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

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

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

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

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

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

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

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

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

A grandiose attempt to develop an integral system of a new, dialectical logic was made by another German philosopher - G. Hegel(1770-1831). In his seminal work, The Science of Logic, he revealed the fundamental contradiction between the available logical theories and the actual practice of thinking, which by that time had reached considerable heights. The means of resolving this contradiction was the creation by him in a peculiar, religious-mystical form of a system of new logic. It focuses on the dialectic of thinking in all its complexity and inconsistency.

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

Topic 2. Language of logic

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

2.1. Correlation of language and thinking. The concept of sign systems.

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

Language- a means of everyday communication between people, a means of communication in scientific and practical activities. The language also has such features: to store information, to be a means of expressing emotions, to be a means of cognition. Language is a sign information system, a product of human spiritual activity. The accumulated information is transmitted using the signs (words) of the language.

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

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

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

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

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

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

Name- this is a language expression denoting a single object, a set of objects, a property or a relation.

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

In logic, a distinction is made between expressions that are named functions and expressions that are propositional functions. Nominal function- this is an expression that, when variables are replaced by constants, turns into a designation of an object. This is the name of an expression that contains a variable and turns into a true or false statement when the name of an object from a certain subject area is substituted for the variable.

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

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

It is possible to single out signs of the following three types: 1) signs - indices; 2) signs - samples; 3) signs - symbols.

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

Sample signs are those signs that in themselves provide information about the objects they represent (a map of the area, a map-drawing), since they are in a relationship of similarity with the designated objects.

Signs-symbols are not connected causally and are not similar to their representation by objects. Logic examines signs of the latter kind.

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

A "predicate" in philosophy and logic almost coincides in its meaning, it is any sign inherent or not inherent in this or that subject, in logic, of course, the subject of thought.

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

P is the symbol of the judgment predicate (logical predicate), i.e. a concept that reflects an attribute inherent or not inherent in the subject of thought (subject).

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

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

R is the symbol of any relation.

A (a) is a symbol of a universally affirmative judgment (“All students are students”).

E (e) is a symbol of a generally negative judgment (“All students in this group are not athletes”, or, which is the same thing, “Not a single student in this group is an athlete”).

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

O (o) - a symbol of a private negative judgment ("Some students are not excellent students").

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

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

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

V is a symbol (sign) of the separating logical union "or" (disjunction).

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

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

"Not" - a negative particle, can also be expressed with a bar over the sign, for example: B, C.

A symbol to indicate a need.

A symbol to indicate an opportunity.

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

names are language expressions whose substitution into the formula "S is P" instead of the variables S and P gives a meaningful sentence.

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

Suggestion (statement) is a language expression that is true or false.

Functor- this is a linguistic expression that is neither a name nor a statement and serves to form new names or statements from existing ones.

Topic 3. Basic laws of logic

3.1. The concept of "logical law"

Law of thought- this is an internal, necessary connection between thoughts. The simplest and at the same time necessary connections between thoughts are expressed with the help of the main formally logical laws, the obedience to which determines the certainty, consistency, consistency and validity of thinking. Formal logic considers four basic laws: identity, non-contradiction, excluded middle, sufficient reason. These laws express the most general properties of all correct thinking and have a universal and necessary character. Without observing these laws, correct thinking is generally impossible.

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

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

3.2. The law of identity and its logical requirements for the thinking process, as well as errors due to their violation

Law of Identity establishes the requirement for the certainty of thinking: using a term in the process of thinking, we must understand by it something definite. Therefore, in reasoning it is necessary to leave concepts and judgments the same in content and meaning. This requirement is preserved if each transformation is nullified by its inverse (zero transformation).

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

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

This brief review shows that the law of identity is universal in the sense of covering all forms of thought without exception, any thought in general.

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

Certain requirements follow from the law of identity, which operates objectively in our thinking.

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

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

Related to this requirement is the following.

2) It is impossible to identify different thoughts and it is impossible to take identical thoughts for different ones.

Requiring certainty, unambiguity of thought, the law of identity at the same time is directed against any fuzziness, inaccuracy, vagueness of our concepts, etc.

In cases where the requirements of the law of identity are violated, numerous logical errors occur. They are called differently: amphibolia"(ambiguity, i.e., the use of the same homonym word at the same time in different senses), "mixing of concepts", "confusion in concepts", "substitution of one concept for another" ( equivocation), "thesis substitution", etc.

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

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

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

3.3. The law of non-contradiction, its constructive role in logical thinking

Law of non-contradiction expresses the requirement of consistency of thinking and reflects the qualitative certainty of objects. From the standpoint of this remark, an object cannot have mutually exclusive properties, that is, it is impossible, at the same time, the presence and absence of any property in an object.

The formula of the law says: It is not true that A and not A are both true at the same time.

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

Thus, judgments cannot be true at the same time: this person is a good specialist - this person is a bad specialist.

The objective content of the law is in the reflection by thinking of the special binomeric features of reality itself. These opposite features, or constructs, make it possible to classify phenomena and highlight positive and negative phenomena. Without doing this, it is impossible to make a distinction from which mental activity begins. The logical source of the contradiction is an erroneous starting position; the result of thoughtlessness and ignorance of the matter; undeveloped, undisciplined thinking; ignorance and the desire to deliberately confuse the matter.

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

1) if we are talking about different features of one object;

2) when it comes to different subjects with one sign;

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

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

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

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

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

The law of non-contradiction is also found in inferences. On it are based, for example, direct inferences through the transformation of judgments. This operation is possible only because the object of thought cannot both belong and not belong to the same class of objects. Otherwise, there will be a logical contradiction. In inferences through the ratio of judgments in a logical square, the law of non-contradiction affects the fact that if any judgment is true, then the one that contradicts or opposes it will be false. In other words, they cannot both be true.

Finally, the law of contradiction operates in the proof. It underlies one of the rules of the grounds of evidence: they must not contradict each other. Without the operation of this law, refutation would be impossible. Having proved the truth of one thesis, it is not possible to conclude the falsity of the opposite or contradictory thesis.

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

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

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

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

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

Logical contradictions are intolerable in everyday speech. A person is no longer respected if, on the same occasion, he says one thing today and another tomorrow. This is a man without principles.

3.4. The Law of the Excluded Middle and Its Importance in Determining Truth

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

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

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

The law of the excluded middle and the law of non-contradiction are related. Both of them do not allow the existence of conflicting thoughts. But there are also differences between them. The law of non-contradiction expresses the relationship between opposing propositions. For example: "This paper is white." “This paper is black.” The Law of the Excluded Middle expresses the relationship between conflicting propositions. For example: "This paper is white." “This paper is not white.” Because of this, in the case of the law of non-contradiction, both judgments cannot be simultaneously true, but they can be simultaneously false, and the third judgment will be true - "This paper is red." In the case of the operation of the law of the excluded middle, both judgments cannot be simultaneously false, one of them will necessarily be true, the other false, and no third, middle judgment is possible. If, on the other hand, judgments that are contradictory in form do not relate to a single object, but to a class of objects, when something is affirmed or denied regarding each object of a given class, and the same is denied regarding each object of a given class, then the truth relations between them are established according to the rules of “logical square." When one of the judgments affirms something about the whole class of objects or phenomena, and another judgment denies the same about a part of the objects or phenomena of the same class, then one of such judgments will necessarily be true, the other will be false, and the third is not given. For example: “All fish breathe with gills” and “Some fish do not breathe with gills.” Both of these propositions cannot be both true and false at the same time.

Requirements of the law of the excluded middle and their violations. Based on this law, certain requirements for thinking can be formulated. A person often faces a dilemma: to choose not from the same, but from mutually negating statements. The Law of the Excluded Middle just requires a choice - one of two - according to the principle "either - or", tetrium non datur (the third is not given). It means that when solving an alternative question, one cannot evade a definite answer; you can not look for something intermediate, middle, third.

Meaning of the Law of the Excluded Middle. This law cannot specify exactly which of the two contradictory propositions is true. But its significance lies in the fact that it establishes for us well-defined intellectual boundaries in which the search for truth is possible. This truth is contained in one of two contradictory statements. Beyond these limits, it makes no sense to look for it. The very choice of one of the judgments as true is ensured by the means of one or another science and practice.

III. Educational process. 29. A general educational institution carries out the educational process in accordance with the levels of general educational programs of the three levels of education:

III. Educational process. 3.1. The gymnasium implements general educational programs of basic general, secondary (complete) general education

III. Requirements for the structure of the basic educational program of primary general education

III. Levels of the language and sections of the science of the modern Russian literary language

The word "logic" to denote the science of thinking, about its forms and laws, was introduced in the very early III V. BC. the founder of the Stoic trend in philosophy - Zeno from the city of Kition, in Cyprus (c. 336-264 BC) As you know, Aristotle (384--322 BC), the true creator of logic as a science, used the word "analytics" to designate it. Most likely, the word "logic" comes from the ancient Greek "logos", which even then was an extremely ambiguous expression, which is fundamental to philosophical views many ancient philosophers. The ambiguity of the logos was also reflected in the meaning of the word "logic". “Logos” is a concept, word, thought, mind, idea, principle, law, order, etc.

In Russian, the word "logic" is used to refer to:

a) the necessary, regular connection of objects and events in the surrounding world, the connection of the next with the previous (the logic of things, the logic of events, the logic of reality, physical, objective, causal logic, objective logic, etc.);

b) just as naturally interconnected, consistent reasoning, reflection (the logic of reasoning by Ivanov, Petrov or Sidorov, "iron logic", subjective logic, etc.);

c) the science of the forms and laws of thought.

If we talk about logic in the last sense of the word - about logic as a science, then it can be given the following definition. This is the science of the structure of thought forms, of the simplest mental methods, of the laws of connection between thought forms, as well as of the errors that are possible when these laws are violated.

Psychology- features of thinking in the process of human development, in the process of his training, education, work; thinking of groups, classes, nations; conditions for the normal development of thinking, the influence on thinking of other aspects of the psyche; thinking of children, adults, old people, etc.

formal logic- the structure of mental forms and explores them as universal, the same for everyone, regardless of nationality, class, age or historical process.

Physiology higher nervous activity - thinking from the side of the material mechanism of the activity of the human brain, that is, the mechanism underlying the thought processes, without affecting the thoughts themselves.

formal logic- distracting from material mechanisms, he is interested only in thought as such, thought in itself, its structure and connections.

Epistemology And dialectics (dialectical logic), as a branch of philosophy - use the forms and laws of thought to study the process of thinking, its historical formation, its development.

formal logic is abstracted from the history of the development of thought forms and studies only the laws of their internal structure, the laws of their connection with each other.

From the proposed comparison of sciences, the specificity of the subject of logic is quite obvious. Logic studies the forms of thought, as it were, existing on their own, regardless of the means (sign systems) in which thought is expressed, and of those objects that are mentally reflected. Logic does not deny all these connections, but they are not included in the subject matter of the science of logic.

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

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

Etymology of logic

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

Reference Method

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

Logic principle

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

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

If you analyze it, you can see that in each of them the third is explained by two arguments. Although each of the examples belongs to different fields of knowledge, the way of communication constituent parts the content in each of them is the same. Namely: if an object has a certain property, then everything that concerns this quality has another property. Result: The item in question also has this second property. These cause-and-effect relationships are called logic. This relationship can be observed in many life situations.

Let's turn to history

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

Logic originated in ancient China during the Golden Age. Chinese philosophy or, as it was also called, the period of "fighting states". Similar to the situation in ancient Greece, the struggle between the wealthy sections of the population and the authorities also flared up here. The first wanted to change the structure of the state and cancel the transfer of power in a hereditary way. During such a struggle, in order to win, it was necessary to gather around him as many supporters as possible. However, if in ancient Greece this served as an additional incentive for the development of logic, then in ancient China it was quite the opposite. After the kingdom of Qin nevertheless became dominant, and the so-called cultural revolution took place, the development of logic at this stage

it stopped.

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

The main subject of logic

It is difficult to single out one specific value that could generally characterize such ancient science. For example, the subject of logic is the study of the laws of derivation of correct definite judgments and statements from certain true circumstances. This is how Friedrich Ludwig Gottlob Frege characterized this ancient science. The concept and subject of logic was also studied by Andrey Nikolayevich Shuman, a well-known logician of our time. He considered it to be the science of thinking, which explores different ways of thinking and models them. In addition, the object and subject of logic is, of course, speech, because logic is carried out only with the help of conversation or discussion, and it does not matter at all whether it is aloud or “to oneself”.

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

The process of searching for truth

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

deductive logic

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

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

inductive logic

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

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

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

Causal relationship

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

An example can be given: scientists who are exploring outer space and the objects that are there have discovered the phenomenon of a “black hole”. This is a kind of cosmic body, the gravitational field of which is so large that it is able to absorb any other object in space. Now let's find out the causal relationship of this phenomenon: if any cosmic body is very large: (1), then it is able to absorb any other (2).

Basic methods of logic

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

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

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

Modern logic

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

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

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

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

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

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

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

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

2) to indicate the rigor, consistency, patterns of the thinking process; in this case, the following expressions are used: “logic of thinking”, “logic of reasoning”, “iron logic of reasoning”, “there is no logic in the conclusion”, etc.

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

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

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

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

The law of identity. Every statement is identical to itself: A = A

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

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

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

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

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

Judgment - this is a form of thinking that contains the assertion or denial of any position regarding objects, phenomena or their properties.

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

The formation of the science of logic, the stages of its development.

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

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

Moscow State University → State University → University → University of higher education → Educational (educational) institution → Educational institution → Institution → Organization → Subject of public law → Subject of law

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

Reducing the scope of a concept with the addition of new features (that is, expanding the content) does not always occur, but only when the feature is characteristic of a part of the scope of the original concept.

Types of concepts.

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

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

A general concept referring to an indefinite number of elements is called non-registering. So, in the concepts of “man”, “investigator”, “decree”, a lot of elements conceivable in them cannot be taken into account: all people, investigators, decrees of the past, present and future are conceived in them. Non-registering concepts have an infinite scope.

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

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

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

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

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

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

5. Concepts are divided into irrelative and correlative, depending on whether they conceive of objects that exist separately or in relation to other objects.

Concepts that reflect objects that exist separately and are thought outside their relationship to other objects are called irrelative. Such are the concepts of “student”, “state”, “crime scene”, etc.

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

6. Relations between concepts. +++++++++++

comparable concepts. According to the content, there can be two main types of relations between concepts - comparability and incomparability. In this case, the concepts themselves are respectively called comparable and incomparable.

Comparable concepts are divided into compatible And incompatible.

Compatibility relationships can be of three types. This includes equivalence, overlap And subordination.

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

Crossing (crossing). The concepts that are in relation to the intersection are those whose volumes partially coincide. The volume of one is thus partly included in the volume of the other and vice versa. The content of such concepts will be different. A schematic representation of the intersection relationship is in the form of two partially aligned circles (Fig. 2). The point of intersection on the diagram is hatched for convenience. An example is the concepts of "peasant" and "tractor driver"; "mathematician" and "tutor".

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

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

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

Opposite (contrast). Concepts that are in relation to the opposite can be called such species of the same genus, the contents of each of which reflect certain features that are not only mutually exclusive, but also replace each other.

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

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

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

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

There are incomparable concepts in any science. They also exist in legal science and practice: “alibi” and “pension fund”, “guilt” and “version”, “legal adviser” and “independence of the judge”, etc., etc. Incomparability characterizes even, it would seem, , similar in content concepts: "enterprise" and "administration of the enterprise", "labor dispute" - "consideration of a labor dispute" and "body for considering a labor dispute", "collective agreement" and "collective negotiations on a collective agreement". It is important to take this circumstance into account in the process of operating with such concepts, so as not to fall into a comical situation, despite the desire.

Classification of judgments.

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

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

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

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

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

The quality of the bond

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

In affirmative judgments reveals the existence of any connection between the subject and the predicate. This is expressed by means of the affirmative connective “is” or the words corresponding to it, a dash, the agreement of words. The general formula for an affirmative judgment is "S is P". For example: "Whales are mammals."

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

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

By volume of the subject

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

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

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

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

Examples: "Some wars are fair", "Some wars are unfair" or "Some witnesses are truthful", "Some witnesses are not truthful". The quantifier word can also be omitted here. Therefore, in order to determine whether there is a particular or general judgment, one must mentally substitute the appropriate word. For example, the proverb “To err is human” does not mean that this applies to every person. Here the concept of "people" is taken in a collective sense.

By modality

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

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

Compound sentences and their types.

Complex propositions are formed from several simple propositions. Such, for example, is the statement of Cicero: “After all, even if acquaintance with law represented an enormous difficulty, even then the consciousness of its great usefulness should have encouraged people to overcome this difficulty.”

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

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

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

1 Connective judgments (conjunctive) are such judgments that include as components other judgments - conjuncts, united by the link "and". For example, "The exercise of the rights and freedoms of man and citizen must not violate the rights and freedoms of other persons."

2 Disjunctive (disjunctive) judgments - include as components of the judgment - disjuncts united by the link "or". For example, "The plaintiff has the right to increase or decrease the size of the claims."

There is a weak disjunction, when the union “or” has a connecting-separating meaning, that is, the components included in a complex proposition do not exclude each other. For example, "A contract of sale may be concluded orally or in writing." Strong disjunction occurs, as a rule, when the logical unions “or”, “or” are used in an exclusive-separating sense, that is, its components exclude each other. For example, “Slander, combined with the accusation of a person of committing a grave or especially grave crime, is punishable by restriction of liberty for a term of up to three years, or by arrest for a term of four to six months, or by imprisonment for a term of up to three years.”

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

Conditional propositions primarily reflect objective causal, spatio-temporal, functional and other relationships between objects and phenomena of reality. However, in the practice of applying legislation, the rights and obligations of people associated with certain conditions can also be expressed in the form of an implication. For example, “Servicemen of military units of the Russian Federation stationed outside the Russian Federation, for crimes committed on the territory of a foreign state, are criminally liable under this Code, unless otherwise provided by an international treaty of the Russian Federation” (clause 2, article 12 of the Criminal Code of the Russian Federation) .

At the same time, it must be borne in mind that the grammatical form “if [...], then” is not an exclusive feature conditional proposition, it can express a simple sequence. For example, “If the person who directly committed the crime is recognized as the perpetrator, then the instigator is the person who persuaded another person to commit

Types of questions.

Questions can be classified in various ways. Consider the main types of issues that are most often addressed in the legal field.

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

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

3. According to the method of requesting the unknown, clarifying and supplementing questions are distinguished. Clarifying questions (or "whether" - questions) are aimed at revealing the truth of the judgments expressed in them. In all these questions, there is a particle “whether”, included in the phrases “is it true”, “is it really”, “is it necessary”, etc. For example, “Is it true that Semenov successfully defended his thesis?”, “Is there really more people in Moscow than in Paris?”, “Is it true that if he passes all the exams with excellent marks, he will receive an increased scholarship?” and others. Complementary questions (or “to” - questions) are designed to identify new properties of the object under study, to obtain new information. A grammatical sign is an interrogative word like “Who?”, “What?”, “Why?”, “When ?", "Where?" and so on. For example, “How to conclude an agreement for the provision of brokerage services?”, “When was this traffic accident committed?”, “What does the word “sponsor” mean?” and etc

4. According to the number of possible answers, questions are open and closed. An open question is a question that has an indefinite set of answers. A closed question is a question that has a finite, most often quite limited, number of answers. These questions are widely used in judicial and investigative practice, in sociological research. For example, the question “How does this teacher lecture?” is an open question, as many answers can be given to it. It can be restructured in order to “close”: “How does this teacher lecture (good, satisfactory, bad)?”.

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

6. According to the correctness of the formulation of questions, they are divided into correct and incorrect. Correct (from lat. correctus - polite, tactful, courteous) question is a question, the premise of which is true and consistent knowledge. An incorrect question is based on the premise of a false or contradictory judgment, or a judgment whose meaning is not defined. There are two types of logically incorrect questions: trivially incorrect and non-trivially incorrect (from Latin trivialis - hackneyed, vulgar, devoid of freshness and originality). A question is trivially incorrect, or meaningless, if it is expressed in sentences containing obscure (indefinite) words or phrases. An example is the following question: "Does critical metaphysication by abstractions and discrediting the tendency of cerebral subjectivism lead to ignoring the system of paradoxical illusions?"

Types of responses.

Among the answers, there are: 1) true and false; 2) direct and indirect; 3) short and detailed; 4) complete and incomplete; 5) exact (certain) and inaccurate (indefinite).

1. True and false answers. By semantic status, i.e. in relation to reality, answers can be true or false. The answer is regarded as true if the judgment expressed in it is correct, or adequately reflects reality. The answer is regarded as false if the judgment expressed in it is incorrect, or does not adequately reflect the state of affairs in reality.

2. Answers direct and indirect. These are two types of answers, differing in the scope of their search.

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

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

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

Short - these are monosyllabic affirmative or negative answers: "yes" or "no".

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

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

4. Complete and incomplete answers. According to the amount of information provided in the answer, the answers may be complete or incomplete. The problem of completeness most often arises when answering complex questions.

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

“The poem “On the Death of a Poet” was written by M.Yu. Lermontov in 1837 in connection with the tragic death of A.S. Pushkin.

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

5. Accurate (definite) and inaccurate (uncertain) answers! The logical relationship between the question and the answer means that the quality of the answer is largely determined by the quality of the question. It is no coincidence that in polemics and in the process of interrogation the rule applies: what is the question, such is the answer. This means that it is difficult to get a clear answer to a vague and ambiguous question; If you want to get a precise and definite answer, then formulate a precise and definite question.

Types of dilemmas

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

The following main types of dilemmas can be distinguished:

- a simple design dilemma,

– complex design dilemma,

- a simple destructive dilemma,

is a complex destructive dilemma.

An example of a simple constructive dilemma (Socrates' reasoning):

“If death is a transition into non-existence, then it is good. If death is a transition to another world, then it is good. Death is a transition to non-existence or to another world. Therefore, death is a blessing.

A simple constructive (affirmative) dilemma:

If A, then C.

If B, then C.

An example of a complex design dilemma:

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

Difficult design dilemma:

If A, then B.

If C, then D.

An example of a simple destructive dilemma:

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

A simple destructive (denying) dilemma:

If A, then B.

If A, then C.

False B or False C.

False A.

An example of a complex destructive dilemma:

“If he is smart, he will see his mistake. If he is sincere, he will confess it. But he either does not see his mistake, or does not admit it. Therefore, he is either not smart or not sincere.

Difficult destructive dilemma:

If A, then B.

If C, then D.

Not-B or Not-D.

Not-A or Not-C.

An example of a complete inductive inference.

All guilty verdicts are issued in a special procedural order.

All acquittals are issued in a special procedural order.

Guilty verdicts and acquittals are decisions of the court.

All court decisions are issued in a special procedural order.

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

Incomplete induction called a conclusion, which, on the basis of the presence of certain recurring features, ranks this or that object in the class of objects homogeneous to it, which also have such a feature.

Incomplete induction is often used in Everyday life human and scientific activity, as it allows to draw a conclusion based on the analysis of a certain part of a given class of objects, saves time and human effort. At the same time, we must not forget that as a result of incomplete induction, a probabilistic conclusion is obtained, which, depending on the type of incomplete induction, will fluctuate from less probable to more probable (11) .

The above can be illustrated by the following example.

The word "milk" changes by case. The word "library" changes by case. The word "doctor" changes by case. The word "ink" changes by case.

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

Probably all nouns change in cases.

Depending on that

Logic occupies a special place in the system of sciences. The peculiarity of the situation is determined by the fact that logic, like philosophy as a whole, performs a methodological role in relation to other sciences with its doctrine of general scientific (universal) forms and methods of thinking.

IN domestic literature methodology is understood in two ways.

First, as a set of methods used by a particular science. In this sense, it is legitimate to talk about the methodology of physics, chemistry, biology and other sciences, since each science uses one or another set of methods, without having a special doctrine about them in its content. The methods of these sciences are based on those simplest ones that are investigated by logic, although they can also be formed as combinations of them; adapted to the specific subject of their sciences, they acquire originality and the appearance of independence from logical ones.

Secondly, as a doctrine of methods. In this sense, only philosophy and logic have methodology, because philosophy explores the universal method of practical and theoretical human activity, and logic explores the basic universal human and general scientific intellectual methods. Since the method is a system of rules, a system of normative provisions, the methodological in this sense is not only related to methods, but also defining, indicating, normative, metric, i.e. similar to methods. It is this role for all sciences that the logical doctrine of the forms and methods of thinking performs.

What is the usefulness, the practical value of logic? Of course, logic can be understood as a certain intellectual toolkit, which is useful for mental activity. But it can also be understood as the end result of the study of forms of thought, which, as with the accumulated experience of mankind, is useful to get acquainted with. However, logic is neither just a tool nor just a result. It is richer in content than both, it requires complete mastery of oneself and only then gives freedom of action, brings practical benefits, and demonstrates its methodological value. Mastering science is difficult, intellectually laborious. Many, however, treat it as a kind of product, result, toolkit that you just have to pick up and you can already use it effectively and get tangible results. But this is far from true. Science demands more, but only after that can it give its masters freedom of action, i.e. practical usefulness and a sense of the value of the knowledge gained.

Meanwhile, the bulk of young people are formed in our country, after all, not as theorists, not as thinkers, but rather as practitioners, experimenters; in theory, for the most part, they act as dogmatists who know how to find out known sources answers to pre-formulated questions. Such educational practice does not form thinkers. They appear in these conditions only as an exception, as an accident, sometimes due to individual character traits that force the individual to oppose himself to widespread practice. The majority is afraid of science, because it is strong "granite" it for assimilation. Others, on the contrary, are not afraid of her, because they do not know her and therefore they treat her with disdain, believing that if she only takes on her, she will succumb. This does not happen with science. It should be taken up at the right time and not broken with it all your life, because only in this case its dynamic internal changes will not go unnoticed. There is no other way to master science, as soon as in the process of long-term, constant, persistent and intensive intellectual work. That is why the “school” passage of a university or university education gives more significant, noticeable results in mastering logic than spontaneous, (rush or attack) amateur attempts to master it. Since logic is a science, an amateurish attitude towards oneself is unlikely to be forgiven. With its teaching on the basic forms and methods of thinking, it is methodological both in relation to other sciences and in relation to all thinkers.

More on the topic § 3. LOGIC METHODOLOGY:

1. 2. 3. THE PLACE OF THE STOIC LOGIC IN THE HISTORY OF LOGICAL DOCTRINES: ATTITUDE TO THE LOGIC OF THE MEGARIANS, ARISTOTLE AND TO THE MODERN FORMAL LOGIC