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Formal logic- the science of laws and forms of thinking that has developed since the times of (see). Formal (or elementary) logic teaches you to think correctly, observing the unambiguity of thought, the consistency of thought, its certainty, evidence, and consistency. If thinking proceeds internally contradictory, discordant, and inconsistently, then no scientific knowledge, no reasoned reasoning aimed at solving certain issues becomes impossible. ““Logical inconsistency” - provided, of course, correct logical thinking - should not exist either in economic or political analysis."

Formal logic puts forward four basic laws of thinking:

1) The thought must be unambiguous. The law of identity teaches that one must be able to correctly identify and distinguish between things, and that substituting one concept for another is unacceptable. In any reasoning, dispute, discussion, each concept must be used in the same sense.

2) Thought must flow consistently. The logical law of contradiction prohibits contradicting oneself in the process of reasoning and analysis of issues. It is necessary to distinguish the contradictions of incorrect reasoning from the contradictions of living life, dialectical contradictions. The contradictions of incorrect reasoning are unacceptable. It is impossible, for example, to speak of a proposition that is recognized as true at the same time as being incorrect.

3) To the same question, correctly posed and correctly understood, says the law of the excluded middle, it is unacceptable to answer vaguely - neither “yes” nor “no” - evading any definiteness of thought. After the necessary clarification of the question, a definite answer must always be given. Of two contradictory propositions, one is necessarily true, and the other is false, and there is nothing third, or, in other words, A is either B or not B.

4) Thought must flow consistently (the law of sufficient reason). Any thought is correct only when it is justified, when it follows as a consequence from another correct thought, which in this case serves as its basis. Therefore, thinking must be consistent. A is because B is, teaches the law of sufficient reason. So, for example, in a conversation with the first American workers’ delegation, when asked about the possibility of abolishing the foreign trade monopoly, J.V. Stalin replied: “The delegation, apparently, has no objections to the fact that the proletariat of the USSR took away factories and plants from the bourgeoisie and landowners. and railroads, banks and mines.

But the delegation, it seems to me, is somewhat perplexed that the proletariat did not limit itself to this and went further, taking away political rights from the bourgeoisie. This, in my opinion, is not entirely logical, or rather, completely illogical... I think that logic obliges. Anyone who thinks about the possibility of returning the bourgeoisie to its political rights must, if he wants to be logical, go further and also raise the question of returning the factories and mills to the bourgeoisie, railways and banks." This example clearly shows what consistency and logic of thought means. As can be seen from the above four logical laws of thinking, formal logic puts forward as mandatory the most general and elementary patterns of thinking, the most general rules of consistency and logic of thought.

Having established the basic laws and rules of thinking, formal logic then moves on to consider the various forms in which the process of thinking takes place. Concept, judgment and inference - these are the forms of thinking that make up the three main sections of formal logic. In the section on concepts, formal logic establishes the types of concepts, their relationships, logical ways of forming concepts, the relationship between the volume and content of concepts, reveals methods and rules for defining and dividing concepts. In the section on judgments, formal logic examines the composition of a judgment, the main types of judgment, etc. In its most extensive section, formal logic gives the concept of inference, classifies the types and methods of inference, develops the doctrine of syllogisms, the rules of syllogism, the figures of syllogism, shows the meaning and role of deductive and inductive inferences in the process of cognition, etc. Finally, formal logic explores the methods and rules of evidence, reveals the role of evidence in the process of logical thinking.

From an examination of the content and tasks of formal logic it follows that it is, as it were, a grammar of logical thinking. Just like grammar, which establishes the rules for changing words, the rules for combining words into sentences and thus gives the language a harmonious, meaningful character, logic makes it possible to give thinking a harmonious, meaningful character. What is common in grammar and logic is that, abstracting from the particular and concrete, they define general rules and laws that make it possible to correctly combine words into sentences, change words (grammar), construct your thoughts correctly, skillfully combine concepts into judgments, judgments into inferences, etc. (logic).

The laws and rules of formal logic, being such laws and rules without which no cognitive process is possible, are universal, universal to mankind. Logical laws are objective laws of science that reflect the phenomena of the objective world. Like language, they serve the thinking of all people, regardless of class. They cannot and therefore are not class-based, just as there is not and cannot be a class-based grammar. Otherwise, people belonging to different classes would not be able to understand each other. The laws and rules of formal logic are the laws and rules of the natural process of thinking. At the same time, various theories about these laws and rules of logical thinking can and do give a distorted interpretation of the laws of thinking.

Thus, idealists construct formal logic as a purely formalistic science, divorced from objective reality. Therefore, Lenin, speaking about the need to study formal logic, demanded that “amendments” be made to the old logic, that is, to free it from all sorts of distortions and idealistic layers. Formal logic is the “lower mathematics” of thinking, revealing the simplest connections and relationships of things, and in itself it is insufficient for scientific research. A powerful tool of scientific research is the Marxist dialectical method, revealing the most general laws of development of nature, society and human thinking. (For the relationship between dialectics and formal logic, see

1. About formal logic

1. Formal approach to inference

Everyone has some ideas about how one can reason and how one cannot reason; We all, starting at a certain age, know something about the structure of correct reasoning - just as we all know something about the structure of the “things” around us. However, humanity was not satisfied with the knowledge about “things” that everyone has: it created natural sciences - physics, chemistry and others - which made it possible to learn incomparably more about these “things” and study them incomparably deeper.

Likewise, the structure of reasoning has become the subject of a special science called philosophical (formal) logic. For a long time, all logic was identified with formal logic; they were synonyms. Formal logic is a science that studies forms of thought - concepts, judgments, inferences, evidence - from the perspective of their logical structure, that is, abstracting from the specific content of thoughts and isolating only the general way of connecting the parts of this content. Basic The task of F.L. is to formulate laws and principles, compliance with which is a necessary condition for achieving true conclusions in the process of obtaining inferential knowledge.

The beginning of formal logic was laid by the works of Aristotle, who developed syllogistics. Further contributions to the development of F. l. contributed by the early Stoics, and in the Middle Ages by the Scholastics (Peter of Spain, Duns Scotus, Occam, Lull, etc.); in modern times - first of all, Leibniz.

2. Aristotle (384–322 BC) – founder of formal logic

Here logic is presented in the form that it acquired as a result of development along the Western path. This path originates from Aristotle (AristotelhV, 384–322 BC) who not only laid the foundations of logic, but also developed a number of its sections so deeply and with such completeness that then it practically did not appear for 2 thousand years in its development beyond the circle of ideas and concepts outlined by Aristotle. (One of the few exceptions were the works of philosophers of the Stoic school, especially Chrysippus (CrusippoV, 280–207 BC). Their logical ideas are in many ways similar to those that, many centuries later, formed the basis of the logic of propositions. However, these the ideas of the Stoics were not understood at that time (and caused bewilderment among historians of logic back in the middle of the 19th century.) By the way, the very term “logic” (in ancient Greek logikh, from logoV - word, speech, judgment, understanding) was introduced by the Stoics (The word logikh is a substantivized adjective; the noun tecnh – “art” is implied).

2. Concept

1. What is a concept?

Along with the study of reasoning to logic according to long tradition include learning concepts. This tradition is completely justified, since it is concepts that represent the material with which we operate in all mental activity, including reasoning.

A concept is a thought that distinguishes a certain class of “objects” according to certain characteristics. For example: the concept “transparent” identifies a class of objects that do not interfere with seeing what is behind them; the concept of “watch” identifies a class of objects that are instruments for measuring time; the concept of “student” identifies a class of people studying in higher educational institutions; the concept of “triangle” identifies a class of geometric figures consisting of three points that do not lie on the same straight line and three segments connecting these points; the concept of “centaur” identifies a class of mythical creatures with a horse’s body and a human head; the concept of “running” distinguishes a class of methods of movement for humans and animals with a sharp push off the ground or quickly moving their paws; The concept of “surprise” identifies a class of feelings caused by something strange or unexpected.

From the above examples it is clear that it is no coincidence that we put the word “objects” in quotation marks. These were either real material objects or fairy creatures, then geometric figures that are ideal images of real objects, then feelings, then methods of movement. In general, “object” can mean here, in essence, everything that we can think of. (Tracing paper from the Latin objectum).

The use of the word “class” is no less conventional here. Usually this word denotes a collection whose elements are clearly separated from each other. But, for example, in the case of “surprise” there is no such aggregate: the feelings falling under this concept form a continuous spectrum that can hardly be naturally divided into individual elements. (If we try to get out of the difficulty by declaring that surprise is a certain unified feeling, so that the class distinguished by the corresponding concept consists of one “object,” then this will not save the situation: after all, someone who does not master this concept cannot imagine surprise as something unified.) The situation is approximately the same with the concept of “running.” And with the concept of “centaur” a difficulty of a different kind arises, even more serious: here, in reality, nothing at all corresponds to the “objects” that should be included in the “class”. And even with the concept of “student”, not everything is as simple as it might seem. After all, it undoubtedly applies not only to current students, but also to previous and future ones. Does it follow from this that the “class of students” includes not only first-year student Vanya Ivanov, but also his father, who graduated from the university twenty years ago? But what about his younger brother, who may or may not become a student over time? And with fictional students - characters from literary works, for example, Turgenev's Belyaev or Chekhov's Petya Trofimov? Answering these questions is not at all easy.

It is most natural, apparently, to consider that the class distinguished by the concept consists not of objects as such, but of ideas about them - meaning that each element of this class is an idea about one object considered “as a whole” (and not about some of its individual aspects or properties). Then, among the elements of the class corresponding to the concept of “student” there will be an idea of Van Ivanov, and an idea of his father in his youth, and an idea of his younger brother in the future, if he becomes a student, and ideas of Belyaev and Trofimov. Elements of the class corresponding to the concept of “centaur” will be, for example, ideas about the insidious Nessus and the wise Chiron. However, such a clarification will not eliminate all the difficulties (for example, the above-mentioned difficulty associated with the concepts of “surprise” and “run” will remain).

Thus, the above “definition” of the concept contains words whose meaning is rather vague and difficult to clarify. (This applies, of course, to both the word “feature” and the word “representation.”) It follows that this is not really a definition, but only an approximate explanation of the meaning of the term “concept.”

The set of characteristics by which a concept is distinguished is called its content (intension), and the class of “objects” that it distinguishes (or, more precisely, the set of ideas about “objects” it distinguishes) is called its volume (extensional).

Accordingly, the scope of the concept “watch” consists of ideas about all kinds of watches - ancient, modern and those that we only imagine, the scope of the concept “student” - from ideas about current, former, future and fictional students, the scope of the concept “centaur” - from ideas about several centaurs, to whom mythology gave names and individual characters, and non-individualized ideas about “centaurs in general.”

3. Equivalent concepts

2 concepts that differ in content can have the same volume. For example, “isosceles triangle” and “triangle with 2 equal angles” are different concepts, although their volumes are the same: they distinguish the same class, but according to different characteristics. (The opposite case - for 2 concepts to have the same content, but different volumes - is obviously impossible.) Concepts whose volumes coincide are called equal in volume or equivalent. These are, for example, the concepts of “a number divisible by 6” and “a number divisible by 2 and 3”, “the current capital of Russia” and “the city in which A.S. Pushkin was born”.

4. Generalization (generalization)

For example, by eliminating from the content of the concept “centaur” the signs “to have a human head” and “to have a horse’s body,” we obtain a more general concept “ mythical creature" By replacing the attribute “to serve for measuring time” in the content of the concept “clock” with the weaker attribute “to serve for measuring something,” we obtain a more general concept of “measuring device.” Replacing the content of the concept “student” with the attribute “to study in higher educational institution» with a weaker sign “to study in any educational institution”, we get the more general concept of “student”. In the same way, the concepts “polygon” and “geometric figure” are generalizations of the concept “triangle” (as well as the concepts “quadrangle”, “pentagon”, etc.); the concepts “predatory animal”, “mammal”, “vertebrate”, “animal” are generalizations of the concept “wolf”.

A mental operation with the help of which a generalization is formed from a concept, i.e. removing one or more features from the content of a concept or replacing them with weaker ones is also called generalization. We can say, for example, that the concept of “polygon” can be obtained by generalizing the concept of “triangle”.

5. Limitation

The mental operation opposite to generalization, i.e., adding one or more features to the content of a concept or replacing one or more features with stronger ones, is called concept limitation; its result is also called. For example, the concept of “centaur” is a limitation of the concept of “mythical creature”, the concept of “watch” is a limitation of the concept of “measuring instrument”, the concept of “triangle” is a limitation of the concepts of “polygon” and “geometric figure”, the concept of “square” is a limitation of the concepts “rectangle” and “rhombus” (as well as “quadrangle”, “polygon”, “geometric figure”).

When a concept is generalized, its scope expands, and when limited, it narrows. For example, the scope of the concept “mythical creature”, along with centaurs, includes sirens, harpies, Kerberos, etc.; The scope of the concept “polygon”, along with triangles, includes quadrangles, pentagons, etc.

A more general concept is often called generic in relation to a less general one, and a less general concept is often called specific in relation to a more general one.
6. Definition of the concept

A mental operation on a concept, consisting in the fact that it is expressed through some other concepts, is called definition, or determination. (Both of these terms were produced - the first by tracing, the second by direct borrowing - from the Latin word definitio, derived from finis - border, limit. The word "definition" is used mainly in philosophical literature, as well as in some special cases (this is what they call, for example, the first sentence of an article in an encyclopedic dictionary); in other cases, it is preferable to use the word “definition.”) The same name is given to a sentence with the help of which one concept is expressed through others (“A prose writer is a writer who writes in prose,” “An insolvent debtor is a person who does not have the means to pay his debts ", "An isosceles triangle is a triangle that has two equal sides", etc.).

Most often, the definition of a concept consists in indicating some more general - generic - concept (“writer”, “triangle”, “person”, “device”) and additional features that need to be added to its content (“writing in prose”, “having two equal sides”, “studying at a higher educational institution”, “serving for measuring time”). If, in this case, the generic concept is closest to the one being defined (that is, there is no sufficiently natural intermediate concept between them), then they speak of definition through the closest genus and specific difference (definitio per genus proximum et differentiam specificam). These are, for example, the above definitions of the concepts “prose writer” and “isosceles triangle” (while the definitions of the concepts “student” and “clock” are not: for “student” the closest generic concept is not “person”, but “student” ", for "watch" - not "device", but "measuring device"). The definition of a concept through the closest genus and species difference does not have to be unique. For example, a square can be defined either as a rectangle, or a cat. all sides are equal, or like a rhombus, in a cat. all angles are right.

For “everyday” concepts - those with which we deal in everyday life - it is often very difficult to give a definition, and it is not always possible to formulate it with any precision. This is well known to compilers of explanatory and encyclopedic dictionaries. – Definitions of scientific concepts play a much more important role. Scientific thinking deals with such objects, phenomena and patterns, cat. are discovered only through systematic, orderly and purposeful work of thought. At the same time, the results of scientific thinking must be verifiable and objective in nature, that is, not depend on the personality of the person who received them, on his beliefs, tastes, inclinations, likes and dislikes. (We are not talking here, of course, about those human qualities thanks to which he was able to obtain a scientific result: the power of intellect, intuition, knowledge, perseverance, etc.). This can only be achieved provided that for each concept used there is a criterion that allows one to decide reliably whether this or that “subject” is included in its scope (otherwise it will become impossible to comply with the law of identity). And such a criterion - since “objects” in this case, as a rule, are inaccessible to direct contemplation - can only be based on the disclosure of the content of the concept, i.e. on its definition.

7. Tree of Porphyry (232–301)

Porphyry (a student of Plotinus) taught that any body, any thing exists, being involved in 5 characteristics that describe it. This:

3) species difference,

4) stable sign and

5) unstable (or random) sign (accident).

In accordance with this, Porfiry builds his famous classification, which went down in the history of logic under the name “Tree of Porphyry.” Thanks to this tree, one can ascend to more general entities - genera and, conversely, descend to more specific ones.

Let's say the most general essence is substance, genus. This genus can be divided into several species. Substance is either corporeal or incorporeal. Corporeal beings, in turn, are animate and inanimate. Let's consider animate beings: they can be sentient or non-sensing (say, animals and plants). Let's consider sentient beings: they are rational and unreasonable. Let's consider intelligent beings: among them there are people, and among people there are already individuals. Thus, descending the Porphyry tree, one can see an increase in the number of species differences. Some individual, for example, Socrates, has an essence, he has a body, he Living being, animate, rational, etc. You can go further: say, by denying the presence of some kind of essence in Socrates, you go back to a certain species. By removing some of Socrates' individual differences (for example, the bald spot on his head), we come to an understanding of man in general. By removing random features and leaving non-random ones, we come to the idea of a person. By removing rational understanding, we ascend to the animate, etc. Each time the ascent up the tree of Porphyry occurs due to the fact that we remove some characteristics - accidents.

It is clear that the highest divine essence can only be described in apophatic language - because we have discarded all accidents. Only by throwing away all accidents do we come to an understanding of God, that is, that which cannot be defined in any way. The very word “define” means “to set a limit.”

The Tree of Porphyry was very popular in the Middle Ages.

8. Undefined concepts

No science can define all its concepts. After all, to define a concept means to express it through some other concepts; if we want to define these concepts, this will mean that we will have to express them through some third ones, etc. Such a process cannot continue indefinitely, and we will be forced to leave some concepts without definition. Therefore, the initial concepts of any science are indefinable. You just need to strive to ensure that such [primary] concepts are as few as possible and that they are simple enough so that their meaning can be well understood, based on examples and approximate explanations. – In general, the definition of a concept can be useful only when the concepts to which it is reduced are simpler and clearer than the concept itself. In prot. In this case, trying to give a definition is futile verbiage and can confuse matters.

Clarifying the content of a scientific concept can be far from an easy task. It happens that a concept that is familiar to everyone who went to school from childhood turns out to be very complex when analyzing its logical structure, and if it is possible to clarify it, this allows one to achieve greater clarity in the formulation of scientific problems and solve them more successfully. Sometimes different authors use the same term to designate different, albeit close, concepts, and this leads to disagreements and disputes in which it makes no sense to talk about the rightness of one side or the other due to the violation of the law of identity. In such cases, the only way to find out the essence of the matter is to clarify the concepts.

9. Single and general concepts

A concept is called single if its volume consists of one object. Examples of single concepts: “Moscow River”, “Eiffel Tower”, “Alexander the Great”, “Thirty Years’ War”, “number 5”. Concepts that are not isolated are usually called general. When classifying a concept as a single concept, caution must be exercised, remembering that the scope of the concept does not consist of objects as such, but of ideas about them. For example, the concept of “president of the USSR” should hardly be considered unique, although there was only one president in the USSR - M. S. Gorbachev: one can imagine, say, a novel by some writer about a certain fictional president of the USSR. At the same time, the concept of “M. S. Gorbachev, who served as President of the USSR in 1990–91.” – single.

10. Collective concepts

A concept is called collective if the objects included in its scope are collections of some “homogeneous” objects, considered “as a whole.” (Thus, the volume of a collective concept is a class, the elements of which are in turn classes.) Examples of collective concepts: “crowd”, “audience” (in the sense of “listeners of a lecture, report, etc.”), “flock”, "bush", "furniture", "peasantry". Collective concepts do not differ in any fundamental way from the rest. In particular, generalization and restriction operations can be performed on them; for example, the concept “flock of geese” is a limitation of the concept “flock”, “Russian peasantry of the 18th century” is a limitation of the concept “peasantry”, “vegetation” is a generalization of the concept “shrub”. Collective concepts can be single (for example, “1st “A” class of school No. 162 in Novosibirsk”).

11. Concrete and abstract concepts

In traditional logic, a distinction is made between concrete and abstract concepts. Specific concepts are those whose volumes consist of objects: “table”, “birch”, “city”, “student”, etc.

This also includes concepts such as “transparent”, “heavy”, since they correspond to classes consisting of specific transparent or heavy objects. Concepts whose volumes consist of imaginary objects that we imagine are somehow similar to real concrete objects - “centaur”, “unicorn”, “alien”, etc. - are also naturally considered concrete.

The remaining concepts are abstract. These include all scientific concepts (“triangle”, “energy”, “acid”, “mammal”, “feudalism”, etc.), as well as many “everyday” ones (“transparency”, “heaviness”, “running”) ", "surprise", "care", etc.) However, the boundary between concrete and abstract concepts is very arbitrary, and different authors draw it differently: some classify as concrete all concepts expressed by nouns that have a plural (or most of these concepts), others believe that all concepts are abstract.

3. Judgment (statement)

Reasoning is expressed in words. The study of sentences is, generally speaking, a matter of linguistics. Modern linguists also consider “semantic completeness” to be the main features of a sentence. Most often, the “complete thought” expressed in a sentence can represent a judgment (although there are questions, exclamations, orders, wishes, requests).

Any sufficiently rigorous proposition can be stated so that it consists only of sentences that are clearly stated statements about some facts, so that for each such statement one can ask whether it is true or false, and to this question there is an unambiguous answer “Yes” " or not". Only such proposals will interest us in the future; When we talk about judgments, we will always mean that they are just that.

For each proposition A of the type we are interested in, we will now write A = I if A is true (that is, the statement expressed by the sentence A is true) and A = A if A is false. In this case, sentence A can be written both verbally and in some symbolic form, for example:

The Volga flows into the Caspian Sea = And;

Dnieper flows into the Caspian Sea = L;

Whale – mammal = AND;

Whale – fish = L;

6 – even number = AND;

6 – odd number = L;

2 + 2 = 4 = AND;

2 + 2 = 5 = L.

We will call the letter I or L the truth value of the corresponding sentence.

4. Basic logical laws

The 4 laws listed below (they are often called the “basic laws of logic”), of course, do not exhaust all the conditions that any correct reasoning must satisfy; These are only the simplest and most obvious (but important!) patterns. Their observance is not sufficient for the correctness of reasoning, but it is necessary: no reasoning in which at least one of these laws is violated can be considered correct. Let us now turn to their consideration. The inability or unwillingness to clarify the meaning of words is a constant source of errors in reasoning.

1. Law of identity

The law of identity is that when in one argument a thought about the same subject appears several times, we must each time have in mind the same subject, strictly making sure that it is not, voluntarily or unwittingly, replaced by another, in something similar to him.

Example. All people must be responsible for their actions. A one-year-old child is human. è A one-year-old child must be responsible for his actions.

2. Law of contradiction

The law of contradiction is that 2 opposing propositions cannot be true at the same time. (2 statements are called opposite, one of which is the negation of the other.) In other words: no statement can be both true and false.

It follows that no reasoning can be considered correct if it contains 2 opposite statements (an obvious violation of the law of contradiction) or statements that, although not themselves opposite, can be deduced from them 2 opposite statements (hidden violation). Discovering hidden judgment can be difficult.

Thus, a judgment about something is taken into account only when it does not contain mutually negating (i.e., opposite) parts. For example, we cannot consider the judgment “The Volga River both flows and does not flow into the Caspian Sea” as a full-fledged judgment, since it contains parts that deny each other. Similarly, the judgment “Seminarist Vikentyev was both present and not present at the philosophy lesson” is unacceptable.

This also includes statements that, although they do not contain directly opposite parts, allow opposite conclusions from their individual parts. Sometimes such a conclusion is not at all obvious (hidden violation).

Obvious violations of the law of non-contradiction are rare: few people will say, for example, “Ivan Ivanovich has already left and has not left yet,” because his interlocutors will think that he is either not speaking seriously or is not mentally well. But we have to deal with hidden violations very often. Such violations are common in judicial practice; investigators, lawyers and judges constantly have to expose them. But, unfortunately, they are also found in official documents, including legislative acts. Then the laws become unenforceable, and a wide path opens for lawlessness and arbitrariness. Therefore, without eliminating contradictions in legislation, a true rule of law state is impossible.

3. Law of the excluded middle

1. The law of the excluded middle is that of 2 opposing judgments, one must certainly be true and the other must be false. In other words: every statement is either true or false.

For example, of 2 judgments - “seminarist Vikentiev is present at the philosophy lesson” and “seminarist Vikentiev is not present at the philosophy lesson” - one must be true, while the other must be false.

Old logicians, formulating this law, often added to the words “either true or false”: “there is no third option” - in Latin tertium non datur. This is where the name “law of the excluded middle” comes from (sometimes it is also called the law of tertium non datur).

2. In the formulation of the law of excluded middle, it is impossible to replace the word “opposite” with the word “contradictory” (although such a formulation, unfortunately, can sometimes be found in the literature). For example, the statements “A.S. Pushkin was born in Kyiv” and “A.S. Pushkin was born in Kazan” contradict each other, but both of them are false.

3. A consequence of the law of excluded middle is the fact that if we have proven the falsity of a statement, then the truth of the opposite judgment automatically follows from this. This property of the law of excluded middle is used in mathematics to obtain “proof by contradiction”.

4. In essence, we cannot even imagine anything “third”, different from truth and from lies and standing on the same level with them. Therefore, it is difficult to imagine a violation of this law. But in modern constructive mathematics the law of excluded middle is not fulfilled.

5. Task. In the fairy tale, the king ordered the “wise maiden” to come to him “neither with a gift nor without a gift,” hoping that she could not bypass the law of the excluded middle. The girl nevertheless coped with the task: she appeared with a live quail in her hands, gave it to the king, and “the quail fluttered and flew away!” How did the girl get out of the situation (Answer: she violated the law of identity.)

4. The Law of Sufficient Reason

It was formulated quite late - by Leibniz (1646–1716). This law states: one cannot be sure of the truth of a judgment if there is no sufficient reason for this.

Sufficient reason should not be confused with reason. For example, for the statement that the air temperature dropped by 10 degrees overnight, the thermometer readings can be a sufficient basis, although they, of course, cannot be the cause of the cold snap.

Concluding the consideration of the basic logical laws, you should pay attention to the fact that the 2nd and 3rd laws are formulated much more clearly than the 1st and 4th. The reason is not difficult to understand: in the laws of contradiction and the excluded middle, only the concept of truth appears, which is intuitively quite clear, and in the other two laws we are dealing with the incomparably less clear concepts of “one and the same object” and “sufficient reason”.

Economic theory, like any other science, has not only a specific subject, but also a special method of research. The word "method" comes from the Greek methods, which literally means "the path to something." That's why a method can be defined in the broadest sense as an activity aimed at achieving a goal . The method of science, on the one hand, reflects the already known laws of the studied sphere of the surrounding world, and on the other hand, it acts as a means of subsequent knowledge.

Thus, the method is both the result of the research process and its prerequisite. While retaining the properties and laws of the object being studied, it at the same time bears the imprint of the purposeful activity of the subject cognizing it.

The objective turns into the subjective, and vice versa. Typically, a research method is formed on the basis of a certain methodology, which includes a worldview approach, a study of the subject, structure and place of a given science in the general system of knowledge, and the method itself.

During the process of cognition, there is a constant interaction between subject and method. The subject presupposes a certain method of research, and the method shapes the subject.

The first method I used economics, there was a formal logic.

Formal logic - This the study of thought from the perspective of its structure and form.

The founder of formal logic is considered Aristotle, who discovered a unique form of inference (syllogism) and formulated the basic laws of logic. Aristotle's students called this new book "organon", that is, "instrument of knowledge." The term “logic” (“word”, “reason”, “law”) appeared later among the Stoics, and only in the 17th century. in the process of creating dialectical logic, this traditional logic, following I. Kant, began to be called formal.

The simplest category of formal logic is concept- it captures a thought about an object. Usually a concept is defined through a broader concept by adding a species distinction to the generic characteristic.

Judgment -it is a thought that affirms or denies something about something. The form of interconnection of judgments is inference.

Inference is a method of thinking through which inferential knowledge is obtained from some initial knowledge.

The most famous form of inference is syllogism. He claims that if a property R belongs to each of the objects that form a given class, then this property will also belong to any individual object classified in this class.

This is called the axiom of syllogism. Formal logic has developed an extensive set of methods and techniques of cognition. The most important of them are analysis and synthesis, induction and deduction, comparison, analogy, hypothesis, proof, and certain laws of thinking.

Analysis- This a method of cognition consisting in dividing the whole into its component parts,synthesis- a method of combining individual parts into a single whole. Although the simplest method of analysis is also the least satisfactory. This is the method of empiricism. An incorrectly conducted analysis can turn the concrete into the abstract and kill the living. The shortcomings of analysis in the formation of concepts are to some extent eliminated synthesis . However, neither analysis nor synthesis reveals the internal contradictions of the subject and, therefore, does not reflect the self-movement and development of the analyzed object. Therefore, this metaphysical method is not able to indicate the path to finding the beginning of the investigation. Induction and deduction have similar disadvantages.

Induction - this is a method of cognition based on inferences from the particular (special) to the general;

Deduction - a method based on inferences from the general to the particular (special). The weakness of induction is that it cannot strictly substantiate the general, since it proceeds only from consideration of a part of the totality. The disadvantage of deduction is that it cannot strictly justify the general premise.

Plays an important role in formal logic comparison - a method that determines the similarity or difference between phenomena and processes. It is widely used in the systematization and classification of concepts, as it allows you to correlate the unknown with the known, to express the new through existing concepts and categories. However, the role of comparison in cognition cannot be overestimated. It, as a rule, is superficial in nature, reflecting only the first steps of research. At the same time, comparison prepares the preconditions for analogy.

Analogy - This is a method of cognition based on the transfer of one or a number of properties from a known phenomenon to an unknown one. In general form, inference by analogy is written as follows. If A and IN have common properties and A has property C, then B also has property C.

Analogy is a special case of induction. It plays an important role in making assumptions and obtaining new knowledge. Many discoveries in political economy were made by analogy. F. Quesnay, for example, proposed a fruitful analogy between blood circulation in the human body and the movement of commodity and cash flows in the social body. This allowed him to build the first macroeconomic model of reproduction. The study of mechanical equilibrium led A. Cournot to the idea of economic equilibrium. Analogy thus plays an important role in generating new ideas and formulating hypotheses. It greatly facilitates the understanding of complex processes, being the basis of scientific modeling. Often, an analogy allows you to correctly pose a problem, determining the direction of further research.

Problem -This is a clearly formulated question or a set of questions that arose in the process of cognition. Problem formulation is possible before the start of the study, during the study and during its completion. If problems are formulated before the start of the study, such problems are called explicit; if not, then implicit. Methods for solving a problem can be known in advance, or can be found in the process of work. Depending on what is known (the formulation of the problem, a method for solving it, or an answer), a simple typology can be given problem situations(See Table 1-1).

The first case is representative problems (everything is known - the problem, the method for solving it and the answer). The second case is typical school problems (everything is known except the answer). The third case is rhetorical problems - puzzles. The fourth case is classical scientific problems. The fifth case illustrates a situation where a correct understanding of the problem formulation comes only at the end of the study. The sixth case corresponds to the situation when methods of other sciences are used in economics. The seventh situation illustrates a dogmatic theory that has ready-made answers to all problems; the eighth is sophisms, paradoxes, antinomies.

A fundamentally new solution to the problem is facilitated by posing the problem in the form of an antinomy. Antinomy -it is a contradiction in which thesis and antithesis have equal force and rest equally on the same foundations. Formulating the problem in the form of an antinomy allows us to reflect the contradictory development of both a real object and knowledge about it. However, from the point of view of formal logic, the antinomy is unsolvable, since it denies its basic laws.

The limitations of formal logic are also indicated by aporia - a statement that contradicts practical experience.

Statement of the problem in the form of a paradox (antinomy, aporia, or even sophistry) contributes to the birth of hypotheses. Hypothesis- This a method of cognition that consists in putting forward a scientifically based assumption about the possible causes or connections of phenomena and processes. A hypothesis arises when new factors appear that contradict the old theory. The scientific theory consists of a core and a protective belt (see Fig. 1-3).

Core - the most fundamental provisions of the theory; The protective belt is formed by auxiliary hypotheses that specify the theory, expanding the scope of its application.

Proven hypotheses merge with the core, unproven ones serve as the object of polemics with opponents, protecting the core of the theory. For example, the core of Marxism is the labor theory of value, the theory of surplus value, the general law of capitalist accumulation, and their protective belt is the law of the tendency of the rate of profit to fall and other laws.

Under proofIn formal logic, we understand the substantiation of the truth of one thought with the help of others. Formal logic offers universal structure proof. It consists of a thesis, evidence bases (arguments) and method of proof (demonstration).

There are different types of evidence. Depending on its goals, evidence of truth and falsity (refutation) is distinguished; depending on the method of evidence - direct and indirect; depending on the basis of the evidence - theoretical and empirical.

Basic laws of formal logic(see Fig. 1-6):

1. Law of identity (A=A);

2. Law of contradiction (A and A, A Λ A);

3. Law of the excluded middle (A and A, A V A);

4. The law of sufficient reason.

Law of Identity means that each thought must have a strictly defined stable content. It is directed against vagueness and uncertainty in economic thinking. This law prohibits, on the one hand, tautology (when one phenomenon is called by different terms), and on the other, the substitution of some concepts for others. The law of identity focuses on the connection and subordination of categories, a clear distinction between generic and specific characteristics.

Law of contradiction means that two opposing thoughts about the same subject, taken in the same time, relation, etc., cannot be true.

Law of the excluded middle asserts that of two thoughts that deny each other about the same object, taken in the same time, relation, etc., one is certainly true.

Law of Sufficient Reason requires that every true thought be justified by other thoughts, the truth of which has been previously proven.

INTRODUCTION

Logic as the science of thinking.
Laws of formal logic.
Concept as a form of thinking
Logical operations with concepts.
Judgments, their types and relationships between them.
Inference: essence and structure.
Inductive and traductive reasoning.
Argumentation and proof.

CONCLUSION.

INTRODUCTION

Given teaching aid is designed to help students learn to apply various logical operations in thinking, learn to think logically correctly and avoid confusing arguments. It is important for a student to be able to apply knowledge of logic in non-standard situations real life and choosing the right decisions.

LOGIC AS THE SCIENCE OF THINKING

Language is a sign system or a means of expressing human thought. Natural language is the basis of speech and a means of communication between people. Artificial language is more formalized and unambiguous and is used in various sciences.

Semiotics as a general theory of signs and sign systems studies the principles of construction of various languages. The semiotic categories of logic are: signs, as material objects and phenomena that represent other objects and serve for the acquisition, storage, processing and transmission of information.

Non-linguistic signs are indicators, symbols and signals. Linguistic or descriptive terms are used for the purpose of communication and to indicate the name and meaning of a thing. A name is a linguistic expression to designate an object. The name of the object can be simple (tourism, market), complex (monetary system), proper (JSC Mosturizm), general (tour company).

Each name has a meaning - denotation and meaning of the name - concept. A term is a word or phrase that accurately designates a specific object. The meaning of a name is the object designated by this name (manager, tourist). The meaning of a name is a way of denoting the name of an object, a more precise fixation of its content. Tourism denotation corresponds to the concept: travel for the purpose of recreation. Sentences are grammatically integral units of human speech and shells of logical judgments. They carry certain information.

In formal logic, the semiotic category is a judgment (statement) - a narrative sentence. A sentence expresses a thought according to its logical meaning, true or false.

To identify the subject of logic, formalized thinking plays an important role, within the framework of which stable properties and relationships are identified in the objects being studied. Formalization is implemented in natural and artificial languages. The use of arithmetic symbols and programming languages led to the emergence of symbolic or mathematical logic, within which formal analysis based on mathematical methods became the basis for solving complex economic and technological problems. Their solution requires:

Identification of the most common properties and relationships between objects and phenomena;

Fixing the properties and characteristics of the thoughts themselves and the relationships between them.

Relations between thoughts are also studied by logic and are expressed in logical terms: essence (is, are); all (each, none); some (if......, then...; and; or), etc. In the course of meaningful reasoning and assessment of specific data, the basis of our conclusions, along with unconditional deductive conclusions, inductive and traductive (by analogy) inferences are used. The latter, despite their probabilistic nature, are very important for proving and arguing controversial positions.

Logic studies precisely this rational stage of cognition and thinking, its indirect ability to move from old knowledge to new ones, without turning to experience each time. For this purpose, inferential knowledge obtained by reasoning from old knowledge is used. If you know that “where there is smoke, there is fire. There is smoke on the hill. Then the conclusion: “there is fire on the hill” is true if the initial knowledge is true and the requirements of logic are met.

The student must understand that the formation of inferential knowledge is subject to certain laws, like all phenomena in the world. Therefore, the main purpose of logic is to study specific mental laws and rules for achieving true inferential knowledge.

How does logic do this? First of all, by studying the forms, structure and rules of thinking in abstracting them from specific content. In this case, the term “logic” is used in two main senses.

Firstly, to denote the ability, skill, art to clearly, clearly, convincingly and consistently reason, prove and refute various provisions. For example, this includes the ability to use words and sentences accurately, which makes speech clear and understandable. Logic shows that with correct reasoning, the conclusion is a logically necessary consequence of the premises. Therefore, the general scheme of this reasoning takes the form of a logical law. Finally, logic helps to skillfully prove and disprove propositions, formulate and resolve the meaning of a problem, see the essence of errors and tricks in a dispute, and avoid sophistical tricks.

Secondly, logic is a special science that studies forms of thinking from the point of view of their structure, as well as the laws and rules for obtaining inferential knowledge. In this case, logic becomes a toolkit for cognitive action. When defining the boundaries and essence of the subject of logic, one should note its importance within the framework of critical thinking and rational argumentation for making and developing management decisions. Since logic is interested in the form of constructing thoughts, and it is abstracted from the specific content contained in them, this section is called formal logic. Its laws, forms and rules of thinking are discussed in this textbook.

CONTROL QUESTIONS:

What is the content of the concept “language”? What is the difference between natural language and artificial language?
What is the name of an object, its meaning and meaning?
What logical forms of thinking exist?
Name the main stages in the development of logic.

2. LAWS OF FORMAL LOGIC.

1. The concept of logical law.

Nature and society are characterized by the interconnection of objects and phenomena. These connections can be objective and subjective, accidental and necessary, general and particular. The most objective, stable, necessary and essential connections are called law. The laws of nature fix that most durable, repeatable thing that remains in the phenomenon. Man in his development acquired the ability to cognize the world, the subjective image of which must coincide with reality.

For a student, this position is methodological, since he must understand and explain the fact of the substantive coincidence and formal difference between the laws of nature and the laws of logic.

Firstly, all laws are objective in the sense that they reflect the same reality and cannot contradict each other. The laws of thinking and the laws of development of objective reality are inextricably linked with each other.

Secondly, the laws of thinking are, first of all, an internal, stable, essential connection between thoughts. After all, if a person is not able to connect and understand his thoughts, then he will not come to the right conclusion, and people will not understand him. The laws of thinking are ahistorical and universal in nature and are successfully applied in ordinary reasoning.

For formal logic, the four basic logical laws are of greatest importance: consistency, excluded middle, identity and sufficient reason. The content and formulation of the first three laws developed in the works of Plato and Aristotle. The development of the fourth belongs to G. Leibniz. Basic logical laws highlight important properties of correct thinking: certainty, consistency, choice of “either-or”, in some tough situations, validity. They are normative in nature, since only their compliance indicates the correctness of thinking. Violation of laws leads to logical contradictions and the inability to distinguish truth from lies. The fourth law is less normative and has limited application.

Non-fundamental laws of logic include: rules for operating with concepts and judgments, rules for obtaining a true conclusion in a simple categorical syllogism, rules for increasing the likelihood of conclusions in inductive and traductive inferences. The laws of mathematical logic also apply.

The law of consistency expresses the requirement of consistency of thinking and reflects the qualitative certainty of objects. From the perspective of this remark, an object cannot have mutually exclusive properties, that is, it is impossible, at the same time, for an object to have and not have any property.

The formula of the law says: it is not true that A and not A are both true. So the judgment 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 binometric features of reality itself. These opposing signs, or constructs, make it possible to classify phenomena and highlight positive and negative phenomena. Without doing this, it is impossible to make the distinction from which mental activity begins. The logical source of contradiction is an erroneous starting position; the result of thoughtlessness and ignorance of the matter; undeveloped, undisciplined thinking; ignorance and desire deliberately confuse the matter.

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

If we are talking about different characteristics of one object. For example, the absence of a trace of a crime is already a trace.
If we are talking about different objects with the same characteristic.
If we are talking about one subject, but it is considered at different times and in different relationships.

So in the dialogue “State” Plato teaches disputants how to pose questions: is the state good? – and answers them, emphasizing different visions and attitudes towards the good.

The nature of judgment can change dramatically over time. On this occasion, Aristotle writes: “The most worthy of all principles is that in relation to which it is impossible to make a mistake. It must appear as unconditional. This beginning is not a hypothesis. What kind of beginning is this? – It is impossible for the same thing to be and not to be inherent in the same thing in the same sense. This is the most worthy of beginnings” (METAPHYSICS). This position "R(RÙP) is directed against Heraclitus, and against the Sophists, actually denying the contradiction.

For future specialists, it is important to highlight the cognitive and practical significance of the law. Thus, the penetration of a formal contradiction into reasoning or theory makes them untenable, and their elimination brings us closer to the truth.

Refuting consequences that contradict the facts, comparing different points of view allows us to identify the incompatibility of judgments A and not A. To do this, you can use the “reduction to absurdity method,” where the fallacy and inconsistency of the conclusions will become obvious. In other cases, this is an appeal to the context of tasks of resolving implicit contradictions. Consistency and consistency of thinking are the basis for the confident and principled actions of any specialist.

Law of the excluded middle makes stronger demands on judgments and demands not to shy away from recognizing the truth of one of the contradictory statements and not to look for something third between them. “One of the terms of the contradiction must be true,” noted Aristotle. In symbolic form, the law is written “R(RVR): not false, not false; either true or false. This law and its action are not reducible to the future, where an event will either take place or not. The law is alternative in characterizing things, hypotheses and paths Problem solving requires identifying different approaches and determining the true one.

For example, the role of the state in the economy should be strengthened and the liberal course maintained. If one of them is true, then the other is false.

The law of the excluded middle requires clear, precise indications of the impossibility of resolving the issue in the same sense: both “yes” and “no”. Its meaning is that the truth is either in the statement or in its negation according to the rules of classical two-valued logic. At the same time, Aristotle is characterized by a different interpretation of the law:

Logical, about the truth of one of the statements;

Ontological, about the existence and non-existence of an object;

Methodological, about the completeness of the study of the object.

In the latter case, uncertain, transitional situations are taken into account and the truth of one of the contradictory judgments is determined with a certain degree of credibility. When questioning, voting, etc., the application of the law requires taking into account the situation and characteristics of the subject area.

The law of identity establishes a requirement for certainty of thinking: using in the process of thinking term, we must understand something specific by it. Therefore, in reasoning it is necessary to leave concepts and judgments the same in content and meaning. This requirement holds if every transformation is undone by its inverse (null transformation). For example, operation 2+5=7-5=2.

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

Even constant movement and change makes it possible to recognize and identify objects. This objective property of a thing, an event, to retain identity, 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 uncertainty or ambiguity. In conversations, disputes and discussions, the same word is often used to express different thoughts, when concepts that are related and close in meaning are expressed by the same words or phrases.

This leads to their use in different meanings, where the requirement of the law is violated when the following errors are made.

Amphiboly is the ambiguity of linguistic expressions or unnoticed polysemy. So in sophism: “Horned” - the one who has not lost horns has them. You haven’t lost your horns, which means you have them; the meanings “had and didn’t lose” and “didn’t have and didn’t lose” violate the law of identity, although they create the appearance of correct reasoning. Another meaning of this error is the substitution of the thesis, and it is important for the student to show in which cases it is used by an unscrupulous opponent. Substitution of a concept, or equivocation, shows that under the guise of a given concept the same word is used in different meanings. For example, every war is just, intervention is a war, therefore the war is just. Here we will use the term war in different meanings.

It is important for the student to learn that the normative requirement of the law: the reflection of the subject must be stable, strong in our thoughts. At the same time, the thought must retain its content throughout the entire discussion about the subject, because, according to Aristotle, it is impossible to think anything if you do not think one thing every time.

The law of sufficient reason requires that every true thought be justified by other true thoughts. False thoughts cannot be substantiated. Despite some contradictory views on the nature of the law, its generally accepted formula: ... if there is a consequence B, then its basis is A. The law expresses the need for validity of thinking, which reflects the cause-and-effect relationship: one of the fundamental properties of the material world.

It is only on this basis that any position that must be considered reliable must be proven. For this purpose, sufficient reasons must be known by virtue of which it is considered true. A sufficient basis can be: a thought that has been tested by practice, scientific definitions and axioms, reliable facts and personal experience. It is important for the student to generalize the knowledge of the laws of logic and steadily apply them in practice so that the results of mental activity are free of contradictions, true, justified and confirmed by the experience of mankind, enshrined in the laws of science.

CONTROL QUESTIONS:

What are the basic and non-basic formal logical laws?
Who and how first formulated these laws?
What objective trends are reflected by the laws of formal logic? What is their scope?
What is the content and scope of the basic laws of logic?
What errors in thinking are possible when the laws of logic are incorrectly applied?

3. CONCEPT AS A FORM OF THINKING

1. Essence and structure of the concept.

2. The law of the inverse relationship between the content and scope of a concept.

3. Relationships between concepts.

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

Signs are the features of similarity or dissimilarity (difference) of objects. Similar characteristics are called general; they express the identity of objects in some respect. The term “feature” denotes that in which objects are related to each other or different from one another. The role of attributes is played by qualities, properties, connections and relationships. Signs are divided into simple and complex, positive and negative. Positive and negative are only simple signs. For example, a simple positive sign is to be a tourist and vice versa - not to be a tourist. Concepts are divided into individual ones, in which one object is conceived (student Ivanov, the Russian parliament), and general ones, about a multitude of homogeneous objects with the same characteristics (student, tourist, manager).

General concepts are divided into registering, that is, finite in scope (second-year student, tour participant), re-registering and non-collective. Analysis of signs and characteristics is the first stage of concept formation. Thus, in various forms of power: monarchy, democracy, oligarchy, there are similar signs of the power of office and personal power, such as the ability to influence someone in order to change his behavior. Zero concepts represent classes of really non-existent objects, for example, a person who is a tourist and does not move anywhere. The concept is self-contradictory because nothing corresponds to it.

In the thinking of the people, concepts are formed through the perception and processing of the essential properties of objects in them. These broad and vague concepts are then reduced to narrow and delimited ones. So from the concept of power the following concepts were formed: form of government, monarchy, ochlocracy.

This process uses logical techniques: abstraction, comparison and generalization. For example, during comparison, the mental similarity or difference of objects is established based on essential and non-essential characteristics. Thus, the essential features of management make it possible to distinguish it from the totality of management operations.

The concept, as a logical form of thinking, has its own structure, which includes two main elements: content and volume. The content of a concept is its main logical characteristic or mental reflection of the aggregate characteristics that distinguish an object or class of objects.

The content of the concept “gross national product” includes two main features: - to be a general indicator of socio-economic development and, secondly, to reflect the final results of activity. The content is divided into factual and logical, where the first is a real set of objects, on the basis of which there is a generalization and identification of the characteristics of objects in the concept.

Logical content is the concept of a non-existent object. These concepts are abstract and serve for the development of science and practice (world ether, thermonuclear power plant, society of universal abundance). The scope of a concept is a reflection of a class or set of objects that have characteristics that make up the content of the concept. The scope of the concept of “tourism” includes all types of active, dynamic recreation.

The content and scope of a concept are in an inverse relationship. If the volume of a concept increases, then its content decreases accordingly and vice versa. The content of the concept of tourism is narrower than the concepts of equestrian tourism and domestic tourism, since it contains fewer features. It is important for a student to learn to express thoughts more accurately or meaningfully, which is necessary when communicating with clients and processing documents.

The relationships between concepts in terms of their scope are clearly visible in the following diagram:

Compatible: Incompatible

1. Equal volume: A – Commerce 1. Subordination

B - Entrepreneurship A - politics

B – economic

policy

C – national

policy

2. Crossing A - Engineer 2. Contrary –

B – Inventor opposite:

old – young

3. Subordination A- Tourist 3. Contradictory -

B – Backpacker contradiction:

knowledgeable - ignorant

The interrelation of objects of the material world also affects the relationships of the concept. Those who have no concept common features are called incomparable.

Comparable concepts are divided into compatible and incompatible.

Compatible concepts have complete or partial coincidence of volumes. They have no signs that prohibit this. Compatibility includes:

Equivolume, where one and the same object is thought of. The scope of the concept completely coincides: agent, broker, dealer;

Intersection, where there is a partial coincidence of volumes and the presence of a number of common features;

A relationship of subordination, where the volume of a smaller, subordinate concept is part of a larger, subordinate concept: dollar - currency.

Incompatible concepts have relationships: subordination (coordination), where the general generic concept includes two or more concepts: common shares, preferred shares;

Opposite (contrary), where one of the concepts denies the characteristics of another concept;

Contradictions (contradictoryity), where one of the concepts contains some characteristics, while others deny them.

It is important for a specialist to know that relationships between concepts are used in all areas of knowledge and activity where it is necessary to express the meaning of an action as accurately as possible, when processing documentation and drawing up reviews, diagrams and diagrams.

CONTROL QUESTIONS:

What is the meaning of a concept as a logical form of thinking?
What is the relationship between the content and scope of a concept?
What types of concepts are there?
LOGICAL OPERATIONS WITH CONCEPTS.
Definition of concepts.
Division of concepts.
Generalization and limitation of concepts.

A definition is a logical operation that allows you to distinguish the subject being studied from other subjects and establish the meaning of a particular word or term. To reveal the content of the definition, it is important to understand the nature of the logical operation, which is aimed at performing a specific task and fixes the connection of thoughts. The main thing in the definition is to reveal the content of the subject using already known concepts. For example, excise tax is a type of indirect tax on consumer products.

In this case, the concept being defined is designated as definitionendum, then with the help of which it is determined - definition. The importance of definition was emphasized by Socrates, calling it maieutics, the art of generating truth in a dispute. At the same time, the definition answers the question: what is it?

Depending on what is being defined, the object itself or its designation, definitions can be real or nominal.

Real these are definitions of objects, that is, what the object is. For example, a tourist complex is a collection of buildings and services to meet the needs of tourists.

Nominal- denote a particular word or expression. Nominal definitions are simpler and more convenient; they use the words “called”, “called”. For example, economics is the science of economic methods. Nominal definitions help reveal the origin of terms.

Definitions can be explicit, in which definiendum and definition are equal. The most common method of explicit definition, known since the time of Aristotle, is definition in terms of the nearest genus or class of objects. The species we are identifying belongs to this genus. Such a definition contains an indication of the class of objects among which it is necessary to select the desired object. A sign by which it is distinguished from a given class is also necessary.

The essence of the definition is to indicate the closest genus, the type of which is the concept we are defining. For example, cybernetics is the science of controlling complex dynamic systems. A specific species characteristic can be specified in other ways. But it must be related to the nearest genus. Thus, in a genetic definition, a distinctive species characteristic shows the nature of the origin or formation of a concept: a circle is a closed curve formed by the movement of a point.

When working with concepts, you should keep in mind the rules of explicit definition and possible errors.

The definition must be proportionate, that is, the definitionendum and definition are of equal volume. At the same time, one should avoid the mistake of an overly broad definition, when the scope of the defining concept is wider than the scope of the defined one. For example, a fair is a trade. A narrow definition of when dfd is also a mistake. less dfns. For example, a fair is a temporary trade for certain persons.
The definition should not contain a circle, tautology or fixation of the same, through the same.
The definition must be clear, clear and unambiguous. It must be defined through the known, and not contain metaphors or negation. For example, repetition is the mother of learning, etc.

Implicit definitions are widely used in science and practice. Their types include:

Semantic definition, where an object corresponds to a certain designation, through a description of its characteristics. For example, a backpacker is defined by movement, equipment, etc.

A syntactic definition describes an object through the rules for operating with it: o - a number multiplied by another number gives o.

Contextual definition clarifies the content of an unfamiliar word according to the meaning of the entire text or speech. The context here is the reasoning as a whole.

In ostensive definitions, the meanings of words are clarified by showing objects.

The operation of dividing concepts is closely related to the definition of concepts. If with the help of a definition the content of a concept is revealed, then with division its volume is more fully characterized.

Since the scope of a concept represents a known class of objects, during division it becomes clear which subclasses the original universe consists of.

Division concretizes knowledge about objects corresponding to the concept being divided.

The main condition: division must be carried out according to a single characteristic or basis of division. The volume of the concept that is subject to division is called the volume of the concept being divided, and the result is called the terms of division. For example, the concept of a student is divided into the concept of a humanities student and a technical university student. The relationship between class and subclass, genus and species of a concept fixes the taxonomic division. Taxonomy is an arrangement in order. This systematizes the relationship between concepts and distributes them into types based on certain grounds.

Taxonomic division is carried out: according to species, dichotomously and by classification.

Division by species requires a clear distribution of the generic concept into species while maintaining the proportionality of the division, where the volume of the dividing concept must be equal to the sum of the volumes of the members of the division. For example; The concept of tourism is divided into domestic and international. A mistake is the absence of some members of the division or unnecessary opinions in this process. Division is carried out according to one base. With two or more bases, the volumes of the division terms intersect.

The division members must completely exhaust the scope of the concept being divided and be continuous. That is, the division members must be subordinate concepts. Within the framework of the dichotomous division, two contradictory species concepts are identified. It is carried out only on one basis, for example, enterprises operate at a loss or break-even, and is used when it is necessary to establish specific concepts. It is always proportionate, since the terms of division exclude each other.

Classification is the distribution of objects into classes according to the similarities and differences between them. Unlike division, classification is based only on essential characteristics and serves to systematize knowledge. As a result, each object falls into the precisely specified class. Mereological classification allows you to divide a complex object into its component parts. For example, an enterprise is divided into a directorate, production units and support services.

Classifications are scientific, artificial and auxiliary.

Generalization operations and restrictions concepts make it possible to significantly clarify its scope. The logical operation of generalizing concepts is a transition from a specific concept to a generic one, with more volume but less content. Example: liberation war is a war. The limit of generalization in scope is philosophical categories.

Limitation of a concept is the opposite operation to generalization, where the transition from a generic concept to a specific one is accompanied by the addition of the first type of species-forming characteristics. For example, an aircraft is an airplane. The limit of limitation is a single concept. The operations of limitation and generalization are based on the law of the inverse relationship between the volume and content of a concept.

The student’s understanding of concepts and logical operations allows him to correctly reflect and interpret phenomena, and to compose various documentation meaningfully and accurately.

CONTROL QUESTIONS:

What are the main types of relationships between concepts in content and volume?
What logical operations are performed with concepts?
What are the possibilities for a definition operation to fail?
What are the division rules and possible errors?

5. JUDGMENTS, THEIR TYPES AND RELATIONS BETWEEN THEM.

Essence, structure and types of judgment.
Distribution of terms in simple categorical judgments.
Relations between the main types of attributive judgments. Logical square.
Logical connections in complex judgments.

A thought is accessible to other people when it is expressed in linguistic form. The form of expression of statements is sentences. But not every sentence is a statement /judgment/. A question or request does not constitute an affirmation or denial of anything.

Therefore, the linguistic form of a judgment is a declarative sentence in which the connection between an object and its attribute, the relationship between objects or the form of their existence is affirmed or denied.

Judgments are attributive if they affirm or deny the connection between an object or its attribute, the relationship of objects or the forms of their existence. Therefore, propositions are either true or false. Judgments reveal the meaning of concepts through their connection with each other, as elements of the whole. If the concept expresses the objective nature of thinking, then the judgment realizes the active attitude of a person to the environment. It records, first of all, the connections and relationships between objects and their properties.

Expressing relationships between individuals, a judgment implements a communicative function with the purpose of communicating and obtaining new information. To do this, according to I. Kant, it is necessary to use and demonstrate the power of judgment in cognitive and communicative processes.

Logic distinguishes subject, predicate, connective and quantifier in the structure of a judgment. A subject is a logical subject or concept about the subject of a judgment. The subject is designated by the letter S, and denotes new knowledge that needs to be proven. A predicate of judgment is a concept about a feature of an object that denotes known knowledge. Denoted by the letter R. The predicate must be better known than the subject, less problematic, and must be recognized by all participants. For example, management (S) is the science of personnel management (P).

A connective is the relationship between the subject of thought and its properties, expressed by conjunctions (is, essence, incorrect: either, or) and simple agreement of words.

A quantifier is a word that indicates whether a judgment refers to the entire scope of the concept expressing the subject, or to its part. Expressed by the words: “all”, “none”, “some”, etc. For example, “All tourist routes should be interesting.”

All elements of judgment influence the qualitative and quantitative characteristics of judgments and their types. They can be simple and complex, deep and superficial, short and complex. In the very in a general sense judgments are divided into assertoric(judgments of reality) - which speak of the presence (absence) of an object of any attribute. The term “asserto” (confident) indicates that object A has property B. A complex assertoric judgment consists of several simple ones.

Apodictic (judgments of necessity) - reflect a sign that is necessary under all conditions.

A lawyer must think logically. We know the world.

Problematic(judgments of possibility) - reflect the probability of the presence or absence of a particular attribute in an object.

The last two types of judgment are widely considered in mathematical logic.

Each judgment has a qualitative and quantitative characteristic. The term “quality” is used in logic exclusively to characterize the presence or absence of properties in an object, for example: some students study logic.

Based on the quality of judgments, they can be affirmative or negative. Affirmative propositions indicate the presence of a property in an object or the belonging of an object to a subject, that is, S is P.

For example, all tourists are travelers.

Negative judgments indicate the absence of properties in an object, i.e. S is not – is P, or S is not – P.

For example, some entrepreneurs are non-engineers.

The number of judgments means a complete or partial class of objects that are thought in a judgment. Some firms operate profitably.

Based on quality and quantity, simple categorical judgments are divided into

Generally affirmative judgments are general in quantity and affirmative in quality, the formulation of the judgment: All S are P. They are denoted by the letter A.

General negative – general in quantity and negative in quality. Formulation of the proposition: no S is P. Denoted by the letter E.

Particularly affirmative – limited in quantity and affirmative in quality. Formula: Some S are P. Denoted by the letter J.

Partial negative judgments are limited in quantity and negative in quality. Formula: some S are not R. for example: some students do not know logic. They are designated by the letter O.

The letters A, E, J, O, denoting types of judgments, allow you to economically construct a thought.

In order to better understand the meaning of judgments, transform them and build true conclusions, it is important to know how the subject and predicate of a given judgment relate. Do they apply in full or only to some part of their volume? To express the volumetric relations of the subject and the predicate, the operation of distributing terms in a judgment is used.

A term is considered distributed if its scope is wholly included or wholly excluded from the scope of another term. A term is unallocated if its scope is partially included in or excluded from the scope of another term.

In the judgment “All engineers are creators,” the subject is distributed, since the scope of the concept “engineer” is included in the scope of the concept “creators.” The predicate “creators” is not distributed. The distribution of terms in judgments is reflected in the table:

The rule is observed: the subject is distributed in the general predicate in a negative judgment. In addition to the relationship between terms in one judgment, one should keep in mind the relationship between different types of attributive judgments.

It is important for students to select examples and characteristics of comparable and incomparable judgments from educational literature. The relationships between comparable judgments can be clearly traced on the basis of a logical diagram (logical square):

Contradictor

Operations of transformation and reversal are associated with the analysis of the internal structure of a judgment and the connection between statements.

Direct inferences from one premise are a categorical judgment AEJO. Direct inferences are transformed and inverted categorical judgments.

Transformations of a categorical judgment are a change in its quality simultaneously with the replacement of a predicate with a term that contradicts it. This

And all S are P________ J some S are P

No S is not P, some S is not P

E no S is P ABOUT some S are not P

All S are not P, some S are not P

Some birds are not waterfowl

Some birds don't live in water

The reversal of a categorical judgment consists of reversing the places of subject and predicate.

And all S are P________ subject to limitation

Some P's are S

All birds fly

Some that fly are birds

J some S are P E no S is P

Some P's are S, no P's are S's

O. Partial negative judgments are not addressed

Some Ss are not Ps some students don't study logic

Some Ps are not Ss

CONTROL QUESTIONS:

What is the structure and types of attributive judgments?
What relationships between judgments are expressed through a logical square?
What is the essence of the logical operations of transformation, inversion and opposition?

CONCLUSION: ESSENCE AND STRUCTURE

All knowledge about the world is divided into direct (empirical) and indirect (inferential). In the first case, this is the result of direct study of the surrounding world. But most of knowledge is obtained indirectly, inferentially, through logical processing of experimental material.

For example, knowing that all products manufactured for sale are goods, and a car is also a product, we draw a conclusion about its commercial nature. The conclusion about this property is obtained by inference, with the help of which new knowledge is extracted from the content of the initial judgments.

So, inference is a form of thinking through which, from one or more definitions, the truth of which has been proven, a judgment is necessarily derived that carries new knowledge. The structure of an inference contains premises and a conclusion or conclusion.

Parcels- These are judgments from which a conclusion is drawn. They contain known knowledge and must be true. Conclusion) is a new judgment obtained from premises in the course of inferential activity.

TYPES OF CONCLUSIONS:

When obtaining a true conclusion, it is necessary to be strictly guided by the normative requirements of thinking, taking into account the nature of the figures, the rules of terms and premises of inference:

Rules of terms:

No conclusion can be drawn from two negative premises.
No conclusion can be drawn from two particular premises.
If one of the premises is negative, then the conclusion is negative.
If one of the premises is private, then the conclusion is private.

Mode, or aspect, is the qualitative and quantitative varieties of premises and conclusions from them. In total, out of 256 modes, 19 are correct. Mode characterizes compliance with the rules and the truth of the conclusion.

Correct modes:

1 figure: AAA, EAE, AJJ, EJO.

2nd figure: AEE, AOO, EAE, EJO.

3rd figure: AAJ, EAO, JAJ, OAO, EJO.

4th figure: AAJ, AEE, JAJ, EAO, EJO.

When characterizing complex, detailed syllogisms, you should turn to the relevant sections of educational literature. You should pay attention to the types of polysyllogism (progressive and regressive syllogism) and its variety - sorites. When characterizing them, it is necessary to emphasize that they contribute to faster processing of information and problem solving, and simplify the process of assessing the situation and making decisions.

An enthymeme (in the mind) is a categorically abbreviated syllogism in which a premise or conclusion is omitted when it is not necessary to state known truths. For example: All students must study conscientiously, and you are a student.

Conclusion missed... All students must study conscientiously.

Are you student

You must study conscientiously.

When analyzing deductive logic, which allows one to obtain a particular conclusion based on one general and one particular premises, the student should pay attention to Aristotle’s requirements for the structure and rules of inference of a syllogism. A typical form of deduction is a simple categorical syllogism, in which two categorical judgments (premises) related general term, a new judgment is obtained - a conclusion.

All students (S) know logic (P).

Ivanov (S) – student (R)

Ivanov (S) – knows logic (P)

The parcels are connected by a common term - students (M - medium, intermediary). M. - included in the premises, but absent in the conclusion. In the inference, the predicate (knows logic) is wider than the subject in scope. Therefore, the predicate of inference is the greater term, and the subject of inference is the lesser term. Accordingly, premises that include the major and minor terms are called the major premise and the minor premise. Depending on the position of the middle term, the qualitative and quantitative nature of the conclusion depends. There are four provisions of the middle term, which correspond to the four figures of the categorical syllogism:

For example, in the second figure:

Not a single book (P) is a periodical (M).

Magazine (S ) – periodical (M)

A magazine (S) is not a book (P).

The student should parse and remember special rules terms and premises of a simple categorical syllogism.

Shape rules include:

I figure: the larger premise is general, the smaller is affirmative.

Figure II: the major premise is general, one of the premises is negative

III figure: the minor premise is affirmative, the conclusion is particular.

Figure IV: does not give a generally affirmative conclusion.

A deeper understanding of the content of deductive logic is given by the nature of the premises and conclusions given by conditional, conditionally categorical and divisive syllogisms. In a conditional inference, both premises and conclusion are conditional propositions. Its structure: “If A, then B.”

A conditional categorical inference contains one of the premises, a conditional proposition, and the other, a simple categorical proposition. A reliable conclusion, necessarily following from the premises, is given by the affirming and negating modes. His scheme: If A, then B. A

The negating mode allows you to build reliable conclusions from the negation of the consequence and the negation of the basis. For example: If A, then B. not B.

If a student knows logic, then he thinks correctly.

The student is thinking incorrectly.

The student does not know logic.

A probable conclusion is given by inferences where thought moves in the direction opposite to the affirmative mode or the opposite to the denying mode.

In a disjunctive syllogism, one of the premises must be a disjunctive proposition. In a conclusion based on the affirmative-negative mode, negation is produced as a consequence of affirmation.

Science can be fundamental or applied.

This science is applied

Therefore, this science cannot be fundamental.

In a dividing syllogism according to the negating - affirming mode, affirmation is made by negation. For example, A or B. is not – A.

In addition, the student should pay attention to the conditional - disjunctive inference, where one premise is conditional, the other is divisive. This inference is called lematic (presumably blind). It can be a dilemma, a trilemma, etc.

CONTROL QUESTIONS:

What types of inferences are there?
What rules of inference apply to a simple categorical syllogism?
What is the mode of a simple categorical syllogism?
What is a polysyllogism, what is its structure and varieties?
What are the types and what is the structure of complex syllogisms?

7. INDUCTIVE AND TRADUCTIVE INFERENCES.

Inductive inferences are a type of inferential knowledge when it moves from facts to generalizations. Inductive conclusions are formed in the course of practical activity, when comparing similar phenomena and searching for their common cause. Induction is an inference from knowledge of a lesser degree of generality to knowledge of a greater degree of generality. Diagram of inductive reasoning.

Items A, B, C, D have the characteristic P

Items A, B, C, D belong to the class S

Therefore all S are P

The basis of inductive thinking are objective, natural connections and relationships, where objects must be of the same type (of the same class). In inductive inference, even from reliable premises, the conclusion is usually probabilistic.

There is a distinction between complete, incomplete and mathematical induction. Within the framework of complete induction, a conclusion about the properties of a class of objects is made based on the study of its individual parts. Incomplete induction provides knowledge about a class of objects based on the study of part of the objects of this class.

Scheme of inductive inference: Incomplete induction includes:

A 1 has attribute B 1. Popular (enumerative)

A 2 has the characteristic B 2. Scientific (eliminative)

n 3.Statistical

A n has sign B

A 1, A 2,…..An have sign B

If in popular induction objects are selected randomly, then in scientific induction the most typical ones are studied systematically, based on control batches and measurements. This allows us to draw a scientific conclusion about the necessary cause-and-effect relationships and laws. Static induction is an inference from a sample (model) to a set of phenomena and trends. This is a transfer of the relative frequency of occurrence of a characteristic to a wider class of phenomena. The study of random mass phenomena (bankruptcy), unpredictable in particulars, shows their occurrence in the numerical proportions of the whole (the probability of bankruptcy). Mathematical induction speaks about the properties of infinitely large sets without testing the derivation infinitely many times. On this basis, laws, formulas of arithmetic progression and others were established.

A number of methods serve to increase the degree of probability and truth of inductive inferences. With their help, inductive logic establishes cause-and-effect relationships under various conditions of phenomena. To the refined and classified D.S. Mill's methods include: similarities, differences, accompanying changes, residuals, etc. The similarity method is based on the search for a common factor of the phenomenon under study, under various conditions of its detection. By excluding the initial signs from these conditions, it is possible to identify a common factor that will be the cause of this phenomenon.

The formula of method and similarity states that if:

Under conditions A, B, C, phenomenon Q arose

Under conditions A, K, L, the phenomenon Q arose

Subject to A, P, Q a phenomenon arose Q

Probably A there is a reason Q

The method of distinction indicates that if the presence or absence of a characteristic causes or eliminates a phenomenon, then this characteristic is the cause of the phenomenon. So if:

Under condition A, B, C, D, phenomenon d occurs

Under condition A, B, C there is no phenomenon d

There's probably a reason d

The method of accompanying changes indicates the correspondence of some changes and the values of others. A change in a previous circumstance is either its consequence or is in a causal relationship with it.

Under condition A, B, C, D, phenomenon Q exists

Under condition A1,B,C,D there is a phenomenon Q1

Therefore, circumstance A is cause Q

It is important to know that this method has established: the amount of yield depending on climate change, the expansion of bodies due to heating, etc.

When characterizing these and other methods, it is important for the student to avoid a number of mistakes that are most characteristic of inductive inferences. Such errors include: hasty generalization without sufficient grounds, substitution of a causal relationship with certain external phenomena, substitution of the conditional with the unconditional in the form of a hasty generalization without taking into account place, time, etc.

The use of independently meaningful and creatively revised rules of thinking for a specialist is the basis for success in practical activities.

CONTROL QUESTIONS:

What is induction and what are its types?
What is the cognitive role of induction?
What methods are used to establish causal relationships in inductive inferences?
What is the essence of tradition - inference by analogy?
What are the conditions for increasing the probability of inference in traductive inferences?

8. ARGUMENTATION AND PROOF

The ability and need to reasonably prove positions and judgments during polemics, conversations and other forms of communication is an important indicator of correct thinking and professional competence. At the same time, it is important for the student to understand that the content of logical knowledge is necessary for mastering the art of argumentation and rational persuasion.

A proof is a logical method of justifying the truth of a judgment with the help of other true judgments. The content of evidence includes the thesis, the basis (arguments), and the form of evidence or demonstration. A thesis is a judgment or position whose truth needs to be proven. Arguments (reasons) are a method of proof that can take the form of various inferences, for example, deductive ones: a l (M-P)

For proof, inductive inferences and analogies are also used, for example, a l (A has the KMR sign)

a 2 (B has the KR sign)

Thesis, consequence B may have attribute M.

Based on the methods, evidence is divided into direct, indirect and genetic. Direct evidence uses undeniable facts, as well as substantiation of the truth of the thesis with arguments. These are answers to exams, scientific disputes, evidence in court, and more. At the same time, legal evidence, based on facts, is a private judgment and a deductive conclusion cannot be obtained from it. In an indirect proof, they first prove the antithesis and, after being convinced of its falsity, prove the truth of the thesis. The antithesis can be one or more propositions. Depending on this structure of the antithesis, indirect evidence is divided into: apagogical(by contradiction) and dividing.

In the first case, by refuting the antithesis, the truth of the thesis is proven. This path is often used in mathematics, when the theorem on the disjointness of two perpendiculars to one line allows their intersection. The antithesis shows the possibility of lowering two perpendiculars from one point to a straight line, which contradicts the axiom of one perpendicular to a straight line from one point. The antithesis is false, therefore the thesis is true.

A disjunctive proof is based on establishing the truth of a thesis by sequentially excluding all elements of a disjunctive judgment or hypothesis, except one, sufficient argument.

And there is either B, or C, or D - the negating affirmative is used.

And it is not B in the mode of dividing-categorical syllogism.

And don't eat C

In practice, this narrows the scope of who is involved in any incident or the situations leading to it.

Genetic evidence is used in establishing the origin and development of a term concept in scientific and historical research. It is especially important for practice to verify their truth based on authentic sources. At the same time, it is important for the student to understand that the norms of proof are:

Ability to use all types of evidence

Use only true thesis and arguments

Rely on genuine facts relevant to the thesis

Do not use unclear, ambiguous and contradictory theses and arguments

Methods of proof must comply with the laws of logic to avoid possible errors.

Logical errors due to incorrect use of the rules of proof and refutation include paralogisms, sophisms and paradoxes.

Paralogism, or incorrect reasoning, appears as a result of an incorrect conclusion, ignorance of the subject or the laws of logic.

Sophism- this is a deliberate mistake, a deliberate violation of the rules of logic, designed to mislead the enemy, the desire to pass off a lie as the truth. This is “crooked speech” or “imaginary wisdom.” If paralogisms arise by chance, then sophistry is a violation of the rules and a deliberate distraction from the main statement.

Sophistry: “The thief does not want to acquire anything bad.

Acquiring something good is a good thing.

Therefore, the thief means well" hides true meaning the concept of "acquisition".

Paradox- This unusual phenomenon or a statement that is sharply at odds with reality. They arise due to ambiguity and contradictions of the initial principles and norms of knowledge. This is the classic paradox: “What I say is false.” Solving the paradox requires going beyond the level of a given system of viewing an object. At the same time, paradoxes lead to profound discoveries. This is the creation of the theory of irrational numbers, the paradoxes of set theory and much more.

During communication, it is important not only to be able to defend one’s position, but also to refute the position of the interlocutor. This is served by the logical method of refuting or destroying evidence by establishing the falsity of a previously put forward thesis.

The structure of the refutation includes:

Refutation thesis; a proposition that needs to be refuted

Refutation arguments, judgments with the help of which the thesis is refuted

Demonstration - a logical form of constructing a refutation

By analogy with the previous material, the student learns and considers the main types of refutations. To do this, relying on additional educational literature, the student selects examples of criticism of the thesis using refutation by facts, reduction to absurdity and proof of the antithesis. Using the reduction to absurdity formula shows:

If A is B, then C is D. The falsity of the consequence leads to

But C is not D the falsity of the original thesis.

Therefore A is not B

When proving an antithesis (refutation by contradiction), establishing its falsity according to the law of excluded middle indicates the truth of the thesis.

When revealing the technique of criticizing arguments, one should pay attention to their direct (indirect) refutation with the help of experience and facts or through the law of sufficient reason. That is, arguments that require proof are not sufficient grounds.

The falsity of the arguments is indicated by their dubious source.

Criticism of the demonstration speaks of errors in the proof, the lack of a logical connection between the thesis being proven and the arguments. When refuting, you should carefully monitor compliance with the rules of inference. The truth of a refutation is ensured by compliance with a number of normative rules:

Propositions to the contrary are not refuted without careful consideration.

It is necessary to take into account possible errors in our arguments

Direct and indirect methods of refutation should be combined

In addition, the rules regarding thesis, argument and demonstration should be strictly followed.

CONTROL QUESTIONS:

What is the specificity and difference between proof and inference?
What are the structure and types of evidence?
What are the ways to refute arguments?
What are the most common mistakes in proof and refutation?
What is the content of paralogisms, sophisms and logical paradoxes?

CONCLUSION

The proposed short textbook attempts to introduce students to the world of logic, which will allow them to gain initial knowledge about the culture of thinking and use it in practical activities.

QUESTIONS FOR TEST IN LOGIC

What are the prerequisites for the emergence of logic?
What is the logical form of thought? How did it appear?
What does formal logic study?
What is the practical and theoretical significance of logic?
What are the basic principles of dialectical logic?
What do the laws of formal logic mean?
What is a concept? Does every common name denote a concept?
What are the main types of attributes of an object?
Content and scope of the concept, the relationship between them?
By what criteria are concepts divided into types?
What are the main types of relationships between concepts in terms of content and scope?
What are the ways to define concepts explicitly and implicitly?
What is the meaning of the operation of division and classification of concepts?
What is judgment as a logical form of thinking?
What is the structure of the judgment?
What types of judgments are there?
How are the terms distributed in simple attributive judgments?
What is the essence of complex judgments and their types?
How are the relationships between complex statements determined?
What are the types of complex judgments?
What is deductive reasoning?
What is inductive inference?
What is deduction?
What is a simple categorical syllogism and what is its structure?
Rules of terms and their influence on the nature of the conclusion?
Rules of figures and their influence on the nature of the conclusion from them?
What are the modes of a simple categorical syllogism?
Polysyllogism, its essence and structure?
Sorites and its types?
Enthymeme, its main features?
What is induction and how does it differ from deduction?
What are the types of induction?
What is the role of inference by analogy?
The role of analogy in cognitive and practical activity?
Concept, composition and types of argumentation and criticism?
What is a proof and what is its structure?
Direct and indirect evidence and methods for its implementation?
What are the main mistakes in proof and refutation?
What is the meaning of sophistry and logical paradoxes?
What are the tricks in an argument and how to neutralize them?

MAIN LITERATURE

Bocharov V.A., Markin V.I. Fundamentals of Logic. - M., 1999.
Getmanova A.D. Logics. - M., 1995.
Grigoriev B.V. Classical logic. - M., 1996.
Ivlev Yu.V. Logics. - M., 1997.
Ivin A.A. Logics. - M., 1999.
Kirillov V.I. Logic exercises. - M., 1999.
Svetlov V.A. Practical logic. - St. Petersburg, 1997.
Novikov O.A., Uvarov S.A. Commercial logic. - St. Petersburg, 1995.
Ruzavin G.I. Logic and argumentation. - M., 1997.

ADDITIONAL LITERATURE

Berkov V.F. Logic: tasks and exercises, workshop. - Minsk, 1998.
Vinogradova Z.I. Logic of scientific management. - M., 1998.
Getmanova A.D. Logic: vocabulary and tasks. - M., 1998.
Gradova D.I. Logic in business and business communication. - M., 1998.
Ivin A.A., Nikiforov A.L. Dictionary of logic. - ,M., 1998.
Kurbatov V.I. Logics. Rostov-on-Don, 1997.
Novikov O.A., Uvarov S.A. Commercial logic., St. Petersburg, 1995.

Page 4 of 8

CHAPTER III

DIALECTICS AND FORMAL LOGIC

§ 1. The subject of formal logic and its changes in the process of development of scientific knowledge

Since thinking is studied by both formal logic and dialectics, the question arises in what relationship formal logic and dialectics stand, what in thinking is studied by formal logic and what by dialectics, what difference there is in the method of studying thinking by dialectics and formal logic.

All these questions must be resolved to understand the essence of dialectics and its significance for the development of modern scientific thinking. Thinking is studied not only by logic, but also by other sciences, for example, psychology. Psychology studies the mental activity of an individual depending on the conditions in which it occurs; The task of psychology is to reveal the patterns of the thinking process, leading to certain cognitive results. Logic makes the study of these “cognitive results its subject; it studies not the laws of the process of thinking in an individual, but the laws of the achievement of truth by thinking. V. I. Lenin wrote: “ Not psychology, Not phenomenology of spirit, A logic = the question of truth" 1 . This, of course, does not mean that psychology is not at all interested in what cognitive results the thinking process leads to: true or false, but the problem of the truth of thinking is not a special subject of psychology.

Dialectics and formal logic are two sciences that have their own history. Both originated and developed in the bosom of philosophy. How do they relate to each other now, what influence do they have on the development of scientific knowledge? To do this, it is not enough to find out only the meaning of these terms, but also the real content of the concepts contained in them.

Logic arose and developed as an analysis of cognitive thinking, its structure, and laws of functioning. Elements of logical analysis are already found in the writings of Indian Buddhists, Greek pre-Socratic natural philosophers, in fragments of Democritus and the reasoning of the Sophists, in Plato’s dialogues, etc. Aristotle is usually considered the first systematizer and founder of logic as a science, who summed up and critically generalized all previous attempts at research in areas of thinking. In his works, for the first time, all those areas of problems that were later identified in the form of logic were brought together and systematically examined, although neither any clear separation of logical problems, nor the name “logic” itself can be found in his writings. Later commentators on Aristotle's philosophy singled out under the name "Aristotelian logic" sections of his teaching about the categories and laws of thinking, related mainly to the analysis of thinking from the side of its formal content - a description of the structure and types of evidence. But this is not the limit of the logic of Aristotle, who gave philosophical interpretations of the forms of thinking, showed their connection with being, and raised the question of logic as a method of cognition.

In Aristotle's studies, consideration of the categories, forms and laws of thinking is constantly intertwined and mixed with reasoning of a cosmological, physical, psychological and linguistic nature. Of undoubted interest are the logical ideas expressed in his “Metaphysics,” where the main types of being, reflected in categories, are analyzed. Aristotle touched on all the main categories: matter, content, form, possibility, reality, quality, quantity, movement, space and time, etc. In the center was the category of essence, which he considered most fully. Analysis of categories spontaneously led Aristotle to understand them mutual connection, transitions, fluidity.

Aristotelian logic is not something whole and complete. It is a combination of different aspects of the logical analysis of comprehending thinking. Therefore, subsequently its different layers served as the object of further development, clarification and generalizations. The Stoics, who introduced the term “logic” itself, developed a theory of inference, complementing Aristotle’s syllogistic and further formalizing it. Essentially, they laid the foundation for propositional logic. The logical thought of the European Middle Ages went in this direction.

In modern times, the theory of inductive inferences, developed by a number of thinkers, including F. Bacon, was added to Aristotle’s teaching on syllogism. Thus, traditional, or classical, formal logic was formed, the features of which are as follows:

1) It formed an organic part of philosophy, was a unique theory and method of cognition. Its laws served as the basis for the metaphysical method of thinking, its theoretical basis. Its actual logical content consisted of rules and forms of inference.

Traditional formal logic studied the forms of following one judgment from others, the structure and structure of ready-made, formed knowledge on the basis of certain laws: identity, inadmissibility of contradiction, excluded third and sufficient grounds. These laws define the necessary and essential connection that exists between formed thoughts within a certain reasoning. So, law of identity requires unambiguous use of terms in inference. In the same conclusion, the same term must be used in the same meaning. If the terms in a conclusion are not unambiguous, then there cannot be a connection between the premises in the conclusion, and therefore there cannot be a conclusion itself.

Law inadmissibility of contradiction its content has the following statement: if any judgment A from the system of judgments forming a conclusion is true, then a judgment that contradicts the judgment cannot be true in the same system A, i.e. in a certain system of judgments forming a conclusion, they cannot simultaneously be a true judgment A and a contradictory judgment (non- A).

This law does not concern the specific content of judgments; it does not resolve the question of which of the contradictory judgments is true. Inference as a form of following one judgment from others can exist and function normally provided that contradictory judgments are not considered true.

According to the law excluded third, two propositions, one of which denies the other, cannot be simultaneously false; if one of them is false, then the other is true, and vice versa.

Law sufficient reason asserts that the truth of any judgment must be sufficiently justified. On the basis of these laws, logic studied the relationships between judgments in a system of any inference, identifying the forms and rules for following one judgment from others that had previously been formed. Concepts and judgments are considered in it only to the extent and from that aspect of them that is necessary for understanding the consequences of judgments.

By studying the patterns of the succession of one judgment from others, already in traditional logic the so-called logical, or formal, criterion for the truth of judgments was established, which, of course, although necessary, is not sufficient. A judgment can, according to all the laws of formal logic, follow from other judgments (any system can be logically consistent) and at the same time not be objectively true, not correspond to reality. Logical consistency and consistency are only one of the necessary, but by no means sufficient conditions for achieving objectively true knowledge about the phenomena of the external world and the laws of their development.

2) Classical logic was not purely formal; it considered laws and forms of thinking simultaneously as principles of being, and being itself was understood differently by materialists and idealists. In this regard, formal logic from the very beginning of its emergence served as an arena for a fierce struggle between materialism and idealism. In analyzing the structure of evidence and inference, she took as a primary element not a judgment (sentence), but a concept (term), deriving formal relations between terms from real relations.

However, when analyzing forms of thinking, she focused her attention on the formal content, that is, she was not primarily interested in what and how a given form of thinking reflects. It explores the content in forms of thinking that makes it possible to derive something new from existing judgments. For example, from any general judgment of the form: “Everything A essence IN"One can deduce the proposition " WITH There is IN"if it is established that WITH is a class subject A. And this is completely independent of the specific content of these judgments; it is connected with the formal content of these judgments and their relationships. Formal content is objective, it is a reflection of objective laws, the most general and simplest relationships, but is not directly related to the specific properties of any specific object reflected in a particular judgment.

The formal content is extremely broad, it reflects the most general properties and relationships inherent in all phenomena of the material world, therefore it is independent of the specific content of judgments. If the rules of inference are related to more specific content, then the scope of application of these rules is narrower.

Thus, the objective content recorded in the forms of thinking becomes formal if it forms the basis of the rules and forms of following one judgment from others.

Finally, from the beginning of its emergence, logic began to use symbolism to designate formal relations, but in classical logic symbolism did not act as a method for solving logical problems; its use was limited and was of a purely auxiliary nature.

But the development of formal logic did not stop at the level fixed in classical or traditional logic. She was constantly enriched with new results, describing her own subject more and more accurately, deeply and completely. At the same time, the development of formal logic occurred in two main directions. The practice of scientific thinking gave rise to new, previously unknown forms of scientific thinking. Formal logic described their structure, clarified the rules and conditions for following. For example, the development of modern science is associated with the emergence and development of inductive methods of proof. Formal logic examined inductive inferences from the perspective of the relations of premises and conclusions in them, it described various shapes inductive inferences, etc. The development of mathematical and physical knowledge put forward new forms of deductive proofs, formal logic described their structure and structure. This will continue in the future: formal logic, using its own means, will study all emerging forms of scientific thinking, both simple and complex, and in each of them it will find its own subject.

One of the most important tasks of formal logic is to study the content of our thinking in order to use it as a basis for improving previous forms of inference and establishing new ones. Previous forms of inference are improved when new additional conditions are introduced, based on the real content of thinking. A law discovered by science can become the basis for new forms and rules of inference. Laws that reflect the simplest relationships inherent in all phenomena of reality act as the formal content of the inference process in general; other, less general laws underlie one or another type of inference or even a separate form of its specific modification.

There is a misconception that formal logic studies only certain forms of thinking, simple, elementary ones. In reality, all forms of thinking are the object of study of formal logic, but it studies them from one, special aspect. Any form of thinking, for example inference, can be the subject of formal logical analysis. After all, every conclusion consists of judgments that are in various relationships with each other. Between the judgments of any inference there are relations that are subject to formal logical laws. If something is a form of thinking, then it, regardless of what its specific content is, falls within the scope of the study of formal logic, and formal logical criteria can be applied to it. In its own ways and means, formal logic studies all forms of thinking, but with these ways and means it cannot study everything in the forms of thinking.

Formal logic develops not only in connection with the emergence of new forms of thinking, but also as a result of the use of new means and techniques for studying its subject. Thus, a major stage in the development of formal logic was the emergence of a new direction in it - mathematical logic, which was a consequence, on the one hand, of the use of new techniques of logical research, and on the other hand, the study of such forms of proof that previously or in a developed form did not exist at all , or were not analyzed in detail by logic.

Mathematical logic as a scientific discipline arose initially as the application of mathematical means to logical research. The subject of mathematics and the subject of formal logic have much in common. The similarity between the subjects of these two sciences lies in the fact that they are associated with the reflection of extremely general relations in reality, expressed in abstractions, the connection of which with the objective world is complex. The commonality of the subjects of formal logic and mathematics served as a reason for attempts, on the one hand, to derive the content of initial mathematical concepts and axioms from logical propositions, and on the other hand, to reduce the content of the latter to the expression of purely quantitative relations studied by mathematics. Such attempts have not and cannot lead to fruitful results, because no matter how close the subjects of these two sciences are, they are still significantly different.

However, the proximity of the subjects of formal logic and mathematics makes it possible to apply, within certain limits, the method of one science to study the subject of another. This was the case in formal logic and mathematics. Since the subject of formal logic, like the subject of mathematics, includes regular relations and for the purposes of study it can be divided into relatively homogeneous, discrete elements that allow quantitative analysis, since the provisions of formal logic, like mathematics, are a reflection of extremely general forms and relations existing in the material world, to the extent that in formal logic mathematical symbolism can be widely used to express concepts and positions, as well as the relationships between them.

The use of mathematical symbolism for solving logical problems turned out to be very fruitful, because mathematical symbolism makes it possible to highlight the aspect or relationship that interests us in objects and unambiguously determine them. The needs of the development of formal logic required the identification of the simplest and most general forms of relations that exist between judgments in the process of inference; the use of mathematical symbolism contributed to the successful solution of this problem. The development of formal logic required further formalization of the relations it studied, and this in turn raised the question of a broader and more far-reaching formalism and the use of mathematical symbolism to solve logical problems.

The trend towards rapprochement between formal logic and mathematics emerged already in the 15th century. It was started by Leibniz, who formulated only some principles of the top part of mathematical logic, which later became known as the algebra of logic. He wrote a program that was implemented later. Concepts, like statements, must be reduced to some basic ones, denoted by appropriate signs or symbols. From this small number of concepts, all the others can be reconstructed or derived by representing them by a combination of these symbols; the deduction of statements is based on universal rules, which, through the introduction of symbols, are formed similarly to the algebraic rules of calculation. Leibniz's ideas were too new for the 17th century, whose science was not prepared for them. Logicians in the 19th century. (J. Bull, C. Pierce, E. Schroeder, P. S. Poretsky) came to them and began to implement them at a different stage of scientific knowledge.

But the introduction of mathematical methods into logic has not yet given rise to a new formal logic or a new branch in it. This was only the first stage in its formation. The Russian logician P. S. Poretsky, who worked fruitfully in this field in the last century, characterized the emerging mathematical logic as follows: “Mathematical logic is logic in its subject matter, and mathematics in its method” 2 . It was essentially not mathematical logic, but also ordinary formal logic in a symbolic representation (symbolic logic, or algebra of logic), although it was already significantly transformed in the direction of its convergence with mathematics in the form and method of studying its subject.

The second stage of the formation of mathematical logic is associated with the application of formal logic to the solution of mathematical problems. The further development of mathematics required the solution of purely logical questions, that is, the resolution of many mathematical problems led to the improvement and further development of the apparatus of formal logic. A contradiction was created between the needs of mathematics and formal logic, its ability to satisfy these needs in its previous form. Formal logic, even in a symbolic representation, was not an effective logical means of solving such mathematical problems as the solvability or unsolvability of problems by one method or another, the deducibility or non-derivability of certain provisions from premises, the structure and essence of mathematical proofs, the peculiarities of the connection between concepts and theories in them .

All these questions were posed by mathematics, their solution is necessary for the progress of mathematics, but they were logical questions in nature.

Logic was developed in this direction by a number of philosophers and mathematicians: B. Russell and A. Whitehead, G. Cantor, K. Gödel, P. S. Novikov, A. N. Kolmogorov, A. A. Markov and others. The apparatus she created began to be applied to the analysis of scientific knowledge, and here the works of G. Frege, J. Lukasiewicz, R. Carnap, A. Tarski, G. Reichenbach and others played a major role.

What is the peculiarity of the logic that is called mathematical?

She studies her subject by creating specially organized systems - artificial, formalized languages. According to her method, called logistic by Church, knowledge is a language, artificially created, formalized. “The dictionary... of a language is determined by writing down common symbols that will be used. They're called original characters language and must be assumed to be indivisible... A finite linear sequence of source symbols is called formula. According to certain rules, from among all the formulas, correctly constructed formulas... After this, some of the number of correctly constructed formulas are declared axioms. And finally installed (initial) inference rules(or rules of action, or transformation rules), according to which from the corresponding correctly constructed formulas both from parcels are directly output or follows directly How conclusion some correctly constructed formula" 3.

All formal logical calculi are built on this image, and new ones will be built on it. Only the signs, the rules for forming sentences from them, the initial axioms and the rules for transition from one sentence to another change.

This ideal model for constructing knowledge, in other words, a created artificial formalized language, is in the true sense a canon of thinking, serving as a method for analyzing real achieved knowledge; we seem to superimpose this model on the results of real knowledge and try, on the one hand, to understand it from the point of view of this model and build according to it. Logical analysis of theoretical knowledge based on this method has yielded great results both for the development of theoretical knowledge and for practice, in particular for solving problems of transferring the functions of human thinking to a machine.

Cybernetics would be impossible without the creation of a method for analyzing knowledge based on the creation of artificial formalized languages. Based on this method, it is possible to analyze existing knowledge and rebuild it accordingly, expressing it, if possible, in a strictly formalized system.

Modern formal logic is branched into many systems, many of its sections are being developed, and its fruitfulness is beyond doubt. But many questions arise about its nature, relation to mathematics, traditional formal logic and philosophy.

The first question that needs to be resolved is whether formal logic studies thinking, and more precisely, whether it refers to logic or mathematics. So, for example, J. Lukasiewicz writes: “However, it is not true that logic is the science of the laws of thinking. To investigate how we really think or how we should think is not the subject of logic. The first task belongs to psychology, the second belongs to the field of practical art, like mnemonics. Logic deals with thinking no more than mathematics.”4

The answer to this question must undoubtedly be approached more precisely than Lukasiewicz. In the form in which the method of logical analysis has now been formed, its subject is language. And here we agree with the following statement by J. Lukasiewicz: “Modern formal logic strives for the greatest possible accuracy. This goal can only be achieved with the help of a precise language, built from stable, visually perceptible signs. Such a language is necessary for any science. Our own thoughts, not formalized into words, are almost incomprehensible to ourselves; the unexpressed thoughts of other people can only be accessible to a clairvoyant. Every scientific truth, in order to be perceived and verified, must be embodied in an external form understandable to everyone. All of these statements appear to be undeniable truth. Modern formal logic therefore places great emphasis on precision of language. What is called formalism is a consequence of this tendency” 5.

If J. Lukasiewicz recognizes all this as an indisputable truth, then it is not clear why he refuses logic to study thinking. After all, thinking exists in reality, in practice, taking a certain sensually perceived form of signs, language, in which these internal forms, images of things are associated with objects of a certain type (sounds, graphic images, etc.).

If knowledge were not a language, it could not be operated in society. There is no object, the image of which knowledge creates, no person can transfer to another an ax that has not yet been made, the plan of which he has in his head, but he can transfer this plan to him if it has taken a sensory-perceptible form. Man is an objective being and acts only in an objective manner; knowledge acquires an objective character, becoming a language.

Concept of language in modern literature has acquired a very broad meaning and goes far beyond what is usually understood by language when talking about the native language, contrasting it with foreign ones. Indeed, now no one is surprised by the expression of Niels Bohr: “Mathematics is more than science, it is the language of science.” But not only mathematics, but any other science is a language; The peculiarity of mathematics in this case is that it becomes the universal language of science.

The most general definition of language, covering both the so-called ordinary or natural languages that operate with words and sentences, and artificial languages of science, with special symbols, may be the following: language is the form of existence of knowledge in the form of a system of signs. Hence, knowledge itself always appears in the form of some kind of language.

Knowledge, being a language system, forms a unique world that has a certain structure, including the connection between its constituent elements according to known rules. This system has its own laws of construction and functioning, it is continuously enriched with new elements, changes its structure, etc. Traditional formal logic in the study of thinking also proceeded from language, but not artificial, but natural. Aristotle was one of the first philosophers who made language the starting point in the analysis of thinking that cognizes the objective world. And indeed, on the surface, thinking appears as speech. Therefore, for Aristotle, a judgment is a statement that affirms or denies something about something. The judgment itself breaks down into terms, and the categories are the highest kinds of statements.

Mathematical logic with its branches (syntax, semantics) continues this tradition, studying the forms of thought through the analysis of language. But the creation of formalized, artificial languages creates the conditions for a more accurate, comprehensive and deep penetration into one’s subject. Therefore, mathematical logic is “logic that has developed into an exact science using mathematical methods” 6.

Of course, mathematical logic is related to mathematics; moreover, its content often includes some tasks that do not have a general logical content, but are directly related only to mathematics. But now these sections are moving into metamathematics, and mathematical logic at a new stage, using new means, solves those problems that traditionally took place in formal logic.

Some modern authors believe that it is not the only possible formal logical apparatus suitable “for solving any problems of the theory of scientific knowledge, if only the latter require logic” 7 . A. A. Zinoviev considers mathematical logic, which includes the calculus of statements and predicates with some additions, as only a certain fragment of the formal logical theory of scientific knowledge, which “does not take into account all the actual diversity of logical forms and their relationships” 8 .

Let us assume that we agree that the formal logical apparatus is not exhausted by mathematical logic in the specified volume, it will be replenished, but this does not mean that the replenishment occurs by including the content of traditional formal logic. Formal logic can develop in modern conditions only through the creation of formalized artificial languages. Traditional logic as a special scientific logical discipline has lost its significance, since mathematical logic, precisely as formal logic, solved its problems more completely, more accurately and deeply. It can retain its pedagogical significance as a propaedeutic in the study of logic and philosophy; But all attempts to galvanize it as a modern logical theory are doomed to failure.

Unlike traditional, modern formal logic has essentially ceased to be a part of philosophy, it has lost its significance as the basis of a philosophical method of achieving truth, its laws cannot be a universal method of cognition of phenomena and their transformation in practice. Formal logic is not part of the Marxist worldview, but in its true, undistorted form it is not part of a worldview hostile to us.

In the conditions of modern, developed scientific knowledge, formal logic has turned into an isolated branch of science, which, as a result of its recent successes, has branched off from philosophy, just as other sciences (natural and social) emerged from philosophy in their time. The subject of formal logic has become highly specialized, and in this sense it is no different from other sciences (psychology, linguistics, mathematics, etc.). The fact that formal logic studies thinking cannot in itself serve as an argument in favor of the fact that the subject of formal logic is included as an integral part in the subject of Marxist philosophy. Thinking can and is being studied by sciences that have long been no longer part of philosophy. Formal logic studies the special side of thinking, so it cannot claim to be a universal method of cognition. Philosophy studies thinking and its laws in order to reveal the general laws of development of phenomena of the external world, as well as in order to discover the laws of development of knowledge itself, to clarify its relationship to the phenomena of objective reality.

Marxist philosophy relates to formal logic in the same way as to other branches of scientific knowledge (mathematics, physics, biology, psychology, linguistics, etc.). To deny formal logic is as absurd as to deny mathematics, linguistics, etc. Furthermore, Marxist philosophy presupposes the existence of good formal logic, the results of which are as interesting to it as the results of all other special sciences. Of course, formal logic needs and uses categories developed by philosophy. So, for example, formal logic must proceed from a scientific understanding of the truth of its criterion, the essence of thinking and its form, the correct dialectical-materialistic solution to the main question of philosophy, etc. Formal logic itself does not and cannot solve by its method and on the basis of its laws these questions, she has a different subject. But other special sciences also need scientific solutions to philosophical questions to the same extent. Modern physics feels the need for a dialectical-materialist view of the world in the same way as formal logic. Philosophy gives modern physics the scientific concept of matter, motion, space, time, etc. Thus, Marxist philosophy is necessary for formal logic to the same extent as for other sciences.

Some representatives of formal logic build their theories on the basis of the categories of idealistic philosophy, develop the doctrine of the structure of evidence on the basis of positivist or other idealistic epistemology. This, of course, brings great damage to formal logic, just as idealism has a detrimental effect on physics, mathematics, biology, etc. Therefore, formal logic has been and remains the arena of a fierce struggle between materialism and idealism. The task of materialist logicians is to criticize the idealistic foundations in the works of foreign representatives of formal logic.

But just as it is absurd to reject the results of the theory of relativity or quantum mechanics on the sole grounds that some bourgeois physicists, when interpreting these theories, proceed from the categories of idealistic philosophy, it is also absurd to see the desire of some to reject all the results of modern formal logic obtained by foreign scientists, arguing for this only because they proceed from incorrect philosophical premises. Our attitude towards bourgeois scientists was defined by V.I. Lenin in his work “Materialism and Empirio-Criticism” as follows: “The task of Marxists here and there is to be able to assimilate and process the gains that are made by these “orders” (you will not do, for example, either step in the field of studying new economic phenomena, without using the works of these clerks), - and be able to cut off their reactionary tendency, be able to lead my line and fight the whole line forces and classes hostile to us" 9.

These words of V.I. Lenin are fully applicable to foreign specialists working in the field of formal logic. We must take from them everything of value and discard reactionary tendencies towards idealism. Formal logic is then truly scientific when, when considering its subject, it proceeds from the philosophical categories of dialectical materialism.

Unlike other special sciences, formal logic is closest to philosophy, both in its origin (it began to stand out from philosophy relatively recently) and in content: the laws and forms of formal logic, like the laws and forms of Marxist philosophy, are universal character in the sense that they must be observed always and everywhere, regardless of what the content of our thinking is, although adherence to the laws of formal logic in itself does not guarantee the objective truth of thinking. But the laws and forms of formal logic, although they are universal, cannot serve as the basis of a philosophical method and theory of knowledge, since it abstracts from the development of both phenomena of the external world and thinking. When the method of any special science (mechanics, mathematics, physics, biology) turns into philosophical method knowledge, then this method itself becomes one-sided, metaphysical.

The same can be said about formal logic. The method developed to study the process of deducing knowledge from previously formed judgments, when abstracting from the development of knowledge, cannot be turned into a universal method of understanding the phenomena of nature, society and human thinking. The absolutization of the method of formal logic is characteristic of many modern bourgeois philosophers and revisionists, who consider formal logic to be the only science about the laws and forms of thinking.

Modern positivism, declaring that philosophy is a trap, meaning by the latter only formal logic (it does not know any other logic), reduces philosophical problems to formal-logical ones and thereby essentially eliminates philosophy, because formal logic in modern conditions has turned into a special field , which analyzes the “technique” of inferential knowledge. It really does not solve the problem of the relationship between thinking and being, and if it tries to solve it with its own methods and means, it will be far from the requirements of modern science, because as a philosophy, formal logic has long exhausted itself. The liquidation of philosophy in modern, logical positivism appears in the form of replacing philosophy with formal logic.

There is a tendency to present dialectics and modern formal logic as two incompatible systems that exclude one another. Recognition of dialectics leads to the denial of formal logic, and vice versa. This would be the case if two scientific systems had the same subject and built theories about it, one of which is a negation of the other. For example, dialectics, in contrast to formal logic, would believe that from the premises: all people are mortal, Socrates is a man, the conclusion follows that Socrates is not mortal. But dialectics has neither propositional calculus, nor predicate calculus, etc. This is not its field of study at all; it does not have its own knowledge on this issue. These two sciences concern different aspects of scientific-theoretical thinking and, since this word has become fashionable to some extent, they complement each other. Dialectics provides a system of categories that work productively in the process of thinking towards new results, and formal logic is an apparatus that makes it possible to derive from theoretical or empirical existing knowledge, with varying degrees of probability, all possible consequences from it.

But they may ask, how then should one treat the provisions of the founders of Marxism-Leninism, which express opposition to the dialectics of formal logic.

That they are not true? Like all other statements of science, they are true in a certain, limited area, relating to a strictly defined sphere, beyond which they lose meaning and their true content. Yes, the founders of Marxism-Leninism, when developing dialectical logic, contrasted it with formal logic. They noted that formal logic as a method of cognition is limited and is a lower level in comparison with dialectics. Thus, F. Engels wrote in Anti-Dühring: “Even formal logic is, first of all, a method for finding new results, for moving from the known to the unknown; and the same thing, only in a much higher sense, is dialectics, which, moreover, breaking through the narrow horizon of formal logic, contains within itself the germ of a broader worldview” 10. Formal logic and dialectics, as methods of cognition of reality, relate to each other as lower and higher mathematics. The same idea is developed by V.I. Lenin, in particular, in the article “Once More Trade Unions,” when he writes that formal logic “takes formal definitions, guided by what is most common or what most often catches the eye, and is limited to this " eleven .

The founders of Marxism-Leninism showed the limitations of formal logic. At the same time, they meant traditional formal logic, which claimed to be a philosophical method and theory of knowledge. Many philosophers who developed it were idealists in solving the main question of philosophy, separated thinking from the material world, forms of thinking from their content (for example, Kant and the Kantians), and proceeded from an idealistic understanding of truth and its criterion. Representatives of formal logic before Marx and Engels were metaphysicians who considered the forms of thinking in series, outside their movement in the process of development of knowledge. Dialectical logic as a philosophical theory of thinking is the opposite of formal logic and is the negation of the latter.

Of utmost importance are the provisions of F. Engels and V. I. Lenin about the place that formal logic should occupy in the doctrine of thinking. Dialectical logic does not deny the importance of formal logic. Formal logic, in the conditions when dialectical logic arose, loses its former significance as a philosophical method and theory of thinking. Dialectics took everything positive from traditional formal logic, but in the 19th and 20th centuries. to stand on the position of formal logic in the field of philosophical method means to go back to metaphysics, to come into conflict with modern level development of scientific knowledge.

As F. Engels notes, formal logic as a philosophical method of cognition is suitable only for household use; it is helpless when they try to apply it to explain phenomena studied by modern science. But formal logic retains its positive significance as a doctrine of inferential knowledge, of the laws and forms of deducing one judgment from systems of others, previously formed; it forms part of the scientific doctrine of evidence, its forms, structure, and the connections of judgments in it. A nihilistic attitude towards formal logic and its problematics is unusual in Marxism, which limited the subject of formal logic, but did not at all discard it.

Modern formal logic in the symbolic form of its presentation is not some kind of “bad” or “lower” logic, but like any other science it has its own subject and method. It is a field of scientific knowledge that studies thinking from one special aspect. And in this respect, it is no different from other special sciences: it becomes “bad” logic if it claims to be the universal methodology of modern science. Correctly understood formal logic is one of the powerful means of understanding the structure of thinking; the apparatus developed by it is used by a wide variety of sciences.

Thus, the development of logic led to its division into two independent scientific disciplines: on the one hand, modern formal logic, which essentially went beyond the boundaries of philosophy in the field of specialized knowledge, and on the other, dialectics, which functions as a method of movement towards objective truth, that is, it has become logic. Dialectics in antiquity from the very beginning acquired two different forms: it was the art of operating with concepts (Plato) and the theoretical understanding of reality itself and, above all, nature (Heraclitus). These two principles in dialectics seemed absolutely heterogeneous: dialectics teaches either thinking, the art of operating with concepts, or understanding, comprehending the world itself, the nature of its things, and they opposed each other as the logical ontological. But the progress of the movement philosophical thought led to the idea of their coincidence. Dialectics has no other goals than to create and improve an apparatus for scientific and theoretical thinking leading to objective truth. But it turns out that this apparatus is a system of concepts, the content of which is taken from the objective world. Dialectics as an understanding of the nature of things and the art of operating with concepts have the same content.

§ 2. Ideas of dialectical logic in philosophy before Marx

Dialectical logic arose later than formal logic. If the problems of formal logic were determined mainly in antiquity, then dialectical logic arose in XIX century. But certain ideas of dialectical logic also took place in more early period development of philosophy.

The emergence of dialectical logic was prepared by the entire course of development of logical thought. One of the main questions of Aristotle’s logic is the problem of the truth of forms of thinking: “In Aristotle,” wrote V. I. Lenin, “ everywhere objective logic mixed with subjective and so despite the fact that everywhere visible objective. There is no doubt about the objectivity of knowledge. Naive faith in the power of reason, in the strength, power, objective truth of knowledge” 12.

Aristotle always considered forms of thinking to be meaningful; the relationships between judgments in inference, in his opinion, are determined by the connections and dependencies of their substantive content. In Aristotle's logic there is a formulation of the question of the relationship between the individual and the general in the forms of thinking, although he could not give the correct solution to this problem. All this indicates that Aristotle, in his doctrine of forms of thinking, raised the question of dialectics; his logic goes beyond just the formal. But the question of a new logic, different from the formal one, arose with particular force and urgency in the philosophy of modern times.

Already R. Descartes in his “Discourse on Method” understood the insufficiency of formal logic as a method of studying phenomena in the creation of practical philosophy, in the transformation of man into the ruler and master of nature 13. The task is not only to cleanse formal logic of harmful and unnecessary scholastic layers, but also to supplement it with something that would lead to the discovery of reliable and new truths. Therefore, Descartes raised the question of another method of cognition, going beyond the one provided by formal logic. Descartes recognized the insufficiency of formal logic not as a science of correct deduction, but as a method and theory of knowledge.

But Descartes could not overcome the narrowness of formal logic as a method of research, for he tried to go beyond the boundaries of scholastic formal logic, with its doctrine of syllogism, by justifying the existence of intuitive truths, through which man gained knowledge of the most important principles of various sciences. Descartes is undoubtedly right that adherence to the formal rules of syllogism, the most impeccable logical deduction cannot serve as a guarantee of the truth of our thinking. Intuition and the rationalistic criterion of clarity and distinctness are too shaky a basis for the truth of our thinking. Descartes understood not only the limitations of formal logic, but also its strength and power. Formal logic is limited as an art of invention, as a method of obtaining new knowledge, but it is necessary and cannot be replaced by anything, as a science about the rules of connection of ready-made, previously acquired knowledge. Strict deduction according to Descartes is the most important element in achieving knowledge in all sciences.

Another modern philosopher, F. Bacon, approached this issue differently. Usually, when we talk about the role of Bacon in the history of logic, attention is drawn to only one circumstance - F. Bacon enriched formal logic with the doctrine of induction, the method of inductive discovery of the causes of phenomena. There can be no doubt that Bacon occupies a definite place in the history of formal logic. But he is great not because he described the connection of premises in an inductive inference and showed in which case this connection leads to reliable conclusions, but in which only to probable ones. He was least of all interested in the logical connection of premises in inductive inference, whereas this alone constitutes the subject of formal logic in the doctrine of induction.

F. Bacon raised the question of induction not in terms of analyzing the structure of inductive inference, but in terms of searching for a new method of cognition, different from that provided by formal logic. The criticism of syllogism goes in this direction. Bacon never doubted that the connection of premises in a syllogism is correct, that the conclusion that the conclusion of the syllogism gives is actually obtained from ready-made knowledge. He criticizes syllogism for its futility in achieving new knowledge, looking for a reliable method for the formation of new and reliable concepts. The main issue of F. Bacon's logic is the doctrine of the formation of scientific concepts, which form the foundation of knowledge.

F. Bacon criticizes scholastic formal logic for the fact that in it not a single general concept is extracted from observations and experience in an appropriate, reliable way, and that a syllogism can be safely used only when it is based on the first definitions established by induction.

Thus, a syllogism is not a way of forming scientific concepts, but a form of drawing consequences from already formed concepts. A reliable method for the formation of concepts is experience and induction.

F. Bacon's one-sidedness lies in the fact that he did not find a place for deduction in the process of formation of new concepts, in the movement from the known to the unknown.

The study of the process of concept formation and all its components is a task not of formal, but of new logic, the name of which F. Bacon has not yet given. He believed that his “Organon” was nothing more than logic, but a logic that opened up a completely new path for thinking, unexplored by the ancients.

Thus, we see that the doctrine of induction is put by F. Bacon in connection with the process of formation of new concepts, i.e. in terms of a different logic, different from formal, therefore, in the history of the emergence of a new direction in logic, it must be given a place corresponding to its merit.

A peculiar attempt to go beyond the limits of formal logic is Leibniz’s teaching about two kinds of truths: reason and fact. The first are based on the principles of formal logic, in particular on the law of inadmissibility of contradiction in thinking. The necessity of truths of this kind is purely logical: contradiction to the truth of reason is unthinkable. These necessary truths include the principles of mathematics, logic, and everything that follows from these principles as a result of deduction.

The scope of formal logic is limited by Leibniz to the logical analysis of existing knowledge.

But Leibniz did not limit our knowledge to the truths of reason, and the method of obtaining new knowledge was only deduction. In addition to the truths of reason, there are also truths of fact (or empirical, random), based on the law of sufficient reason.

The truths of a fact cannot be deduced in a purely logical way according to the law of inadmissibility of contradiction; they are comprehended by a different method and on the basis of another law - the law of sufficient reason, which in his philosophy did not have such a formal logical interpretation as it later received in books on formal logic. For Leibniz, the requirements of the law of sufficient reason are not limited to the fact that the premises in a conclusion must be a sufficient basis for the conclusion; it has a more general meaning: both the law of being (everything that exists must be based on a sufficient basis) and the general law of knowledge (all knowledge arises on a sufficient basis).

The law of sufficient reason was put forward by Leibniz not to justify the logical necessity of a consequence from premises in a deductive conclusion, not to explain logical analysis (he believed that the law of inadmissibility of contradiction was quite sufficient for this), but to justify the logical synthesis that is inevitably encountered in the formation of concepts about natural phenomena, about physical laws, more specifically, to explain the synthesis that occurs in induction. Thus, the law of sufficient reason shows the legitimacy of induction as a means of concept formation.

Leibniz's division of truths into two types - reason and fact - rests on a metaphysical understanding of the essence of knowledge, a rationalistic belittlement of the role of experience and induction, but at the same time it is evidence of Leibniz's desire to go beyond the narrow limits of formal logic in explaining the process of thinking, to isolate such aspects in knowledge, for interpretations of which the laws of formal logic are insufficient.

The further development of the idea of dialectical logic is associated with Kant’s division of logic into general, or formal, and transcendental. This division contributed to a more precise definition of the subject of formal logic and the scope of its application. Kant correctly set the task - to free general or formal logic from what does not constitute its subject: from psychological sections about various cognitive abilities(imagination, wit, etc.), from philosophical sections on the origin of knowledge and various types of reliability of our knowledge, etc. He rightly notes that the expansion of the sphere of formal logic due to problems unusual for it is the result of a misunderstanding of the nature of this science and leads to distortion.

Formal logic should not and cannot study the process of emergence and formation of ideas and concepts; it studies their relationship to each other in some system from the point of view of the agreement of this system with the logical form 14. General logic is the logic of reason, the sphere of which is not the object, but only the forms of the concept of the object.

General logic is only a canon, not an organon of thinking. When it is used as an organon, then only the appearance of objectively true knowledge is obtained. Formal logic, used as an imaginary organon, is called by Kant dialectics or the logic of imaginary truth (appearance), i.e. sophistry.

Kant's teaching on general logic is dual in nature. On the one hand, Kant is the founder of apriorism and formalism in the interpretation of the essence of formal logic. It is from Kant that the interpretation of forms of thinking as pure, absolutely independent of any objective content and arising before any experience (a priori) originates. For Aristotle, the forms of knowledge were also forms of being itself; the relationship between judgments in inference was considered by him as a reflection of real relationships. In the logic of rationalism (Descartes, Leibniz), the forms of thinking were not yet “cleansed” of any objective content.

Rationalism proceeded from the fact that the forms of thinking are not only not alien to the subject content, but also express its essence, that the subject and the forms of thought coincide. Rationalism is associated with the recognition that forms of thinking are forms of comprehending the truth about an object, therefore they have, even if general and too abstract, but objective content. Kant broke with this tradition in logic coming from Aristotle, and laid the foundation for the logic of “pure,” a priori, contentless forms, which found its many adherents abroad in the second half of the 19th and first half of the 20th centuries.

But, on the other hand, Kant’s understanding of the subject of formal logic and the scope of its application played positive role. Before Kant, the scope of formal logic was not strictly defined, and this hindered progress both in the field of formal logic and the emergence of a new logic. Without strictly defining the subject of formal logic, it is impossible to clarify the boundaries of the application of its criteria, their role in achieving truth and in understanding the laws of the cognitive process.

By limiting the subject of formal logic and the scope of its application in achieving truth, Kant creates the prerequisites for the progress of formal logic itself. But, what is also very important, a strict delineation of the subject of formal logic and an understanding of the boundaries and scope of its application had an extremely beneficial effect on the formation of a new logic.

In addition to general logic, in Kant’s system of criticism there is also transcendental logic, which deals not only with form, but also with objects of knowledge. The ideas of transcendental logic occupy a central place in his Critique of Pure Reason. Kant limited the scope of formal logic, showed the negative, negative nature of its criterion precisely in order to proclaim and justify the need for the existence of another logic. Kant's transcendental logic is different from formal logic; it treats issues that are not included in the subject of formal logic. Formal logic abstracts from any objective content, transcendental logic - only from empirical content and explores pure objective thinking. The scope of formal logic does not at all include the study of the origin of knowledge; it takes the formed concepts and judgments, examining only the form of rational thinking; transcendental logic studies the origin and development of concepts that a priori relate to objects. Based on the recognition of the existence of knowledge that does not originate from experience or from pure sensitivity, Kant considers transcendental logic as a science that determines “... the origin, scope and objective significance of such knowledge...” 15. This logic “deals only with the laws of reason and reason, but only insofar as it relates a priori to objects...” 16.

Assessing the essence of Kant’s transcendental logic, one of the major researchers of Kant’s philosophy, V.F. Asmus, writes: “Kant’s transcendental logic was the first - still far from clear and insufficient, but nevertheless a positive outline or outline of dialectical logic” 17. And this is very true, Kant’s transcendental logic is the beginning of dialectical logic, but already at the very beginning it was distorted by apriorism.

Kant's idea that there must be a logic, the subject of which will be the study of development, genesis human knowledge, the process of concept formation, is very true. Kant's desire to make this logic a doctrine of the synthetic essence of human knowledge is also fruitful. Formal logic deals with analysis, transcendental logic deals with synthesis, the formation of new scientific concepts about the subject. The application of the general ideas of transcendental logic to the specific solution of individual logical problems has yielded some positive results; in particular, there is a lot of value in Kant’s understanding of the categories, which in Kant’s philosophy form a whole system (table). The order of categories in this system is not random, but is established on the basis of a certain principle. Many correct thoughts were expressed by Kant about the function of categories in judgment, about the relationship between concept, judgment and inference in the process of development of thinking, about the connection between different forms of judgment 18.

But the defects of the method of criticism itself, apriorism and formalism, left their mark on the nature of the implementation of these fruitful ideas. Kant spoke about the genetic deduction of knowledge, but only a priori. Transcendental logic is the science of the synthetic nature of human knowledge, but only of pure synthesis, which has its basis in an a priori synthetic unity. Categories represent an integral system, but its source lies not in the subject, but in the mind as a certain whole, the unity of all forms, categories and definitions.

The ideas of Kant's transcendental logic found their further development in Hegel's logic. The ideological kinship between Kant’s logic and Hegel’s logic is not difficult to discern, and Hegel himself did not hide it. But compared to Kant, Hegel made a huge step forward in the positive development of the ideas of dialectical logic. If in Kant in the form of transcendental logic we find only a vague outline of dialectical logic, then Hegel quite clearly and definitely outlined the ideas of dialectical logic on an idealistic basis.

Hegel differed little from Kant in his understanding of the subject of formal logic and its meaning. He believed that Aristotle's infinite merit lies in the fact that the latter was the first to undertake a natural-historical description of the phenomena of thinking. Just as naturalists describe various types of animals and plants, Aristotle described forms of thinking, so his logic is the natural history of finite thinking 19 .

Hegel sees the merit of formal logic in general and Aristotle in particular in the fact that it separated the forms of thought from their mother and fixed its attention on the forms in this separation. This, of course, entails the danger of their separation from material content, as was the case in Kant’s logic.

But Hegel also saw the limitations of formal logic, which lie in its very nature. This limitation consists of abstraction, separation of the essential from the accidental, and processing of representation into generic and specific concepts. Rational activity, according to Hegel, is necessary, but not sufficient. Reason also enters into speculative philosophy, but only as a moment on which it does not stop 20. The creator of rational logic himself, Aristotle, thought not only according to the laws and forms of this logic, he would not have put forward any of the judgments he put forward, could not have taken a single step further if he had adhered to the forms of this ordinary logic 21. This logic is insufficient in moving our thinking towards truth.

Formal logic, based on rational activity, considers the forms of thinking in their immobility and difference; it only lists the types of judgments and conclusions, categorizes them, taking care that none of them is forgotten and all are presented in the proper order.

In Hegel's logical views one cannot help but note a certain nihilism in relation to formal logic. Correctly criticizing the metaphysical method, with which the formal logic of that time was organically connected, Hegel was inclined to completely identify metaphysics and formal logic; he did not see the main tendency in the development of formal logic, leading to its isolation into an independent field of science, to its separation from philosophy and, therefore, to liberation from metaphysics.

Hegel somewhat underestimated the role of studies of formal relations in inference, considering Leibniz's thoughts on combinatorial calculus fruitless. His criticism of the ideas of logical calculus 22 shows that a certain and important trend in the development of formal logic - its rapprochement with mathematics, was for him, at least, incomprehensible, and philosophically absolutely fruitless.

Recognizing some significance of formal logic, Hegel called for “to go further and recognize partly the systematic connection, and partly the value of these forms” 23. The result of this further movement in the study of forms of thinking was his dialectical logic, the tasks and features of which he sees in the following: dialectical, or, as he also said, speculative logic, in contrast to formal or rational, studies forms of thinking as forms of true knowledge. Formal logic examines the logical correctness of thinking, and not objective truth in its entirety.

Considering the forms of thinking from the point of view of expressing truth in them means that these forms themselves are meaningful. Hegel proceeded from the fact that “...thinking and its movement are themselves content, and, moreover, such interesting content as can possibly exist” 24, and “...the science of thinking is in itself a true science” 25.

From these positions, he criticizes the Kantian interpretation of the forms of thinking, according to which the latter do not have any content: on the one hand, the “thing in itself,” and on the other hand, as something completely alien, the mind with its subjective forms. But criticism of Kant’s apriorism is carried out by Hegel from the standpoint of an idealistically interpreted identity of thinking and being. Forms of thinking are true and meaningful because apart from them there is no true content at all.

Forms of thinking provide truth not in their isolation from each other and immobility, but in a moving and developing system. Therefore, dialectical logic considers the forms of thinking in their mutual connection and development. Forms of thought achieve truth only because they move and develop in the direction of discovering the essence. In connection with. With this, Hegel establishes a certain subordination between the forms of thinking: concept, judgment and inference. The movement goes from the concept, in which its moments (universal, particular and individual) are not divided, to judgment, where the concept is split into its own moments, and from it to inference as the unity of concept and judgment. In the conclusion, the unity of the moments of the concept is not only restored, but also justified.

Consideration of various forms of thinking in development makes it possible to evaluate their cognitive meanings, which constitutes one of the aspects of dialectical logic.

And finally, dialectical logic, according to Hegel, should reveal the dialectics of the very structure of forms of thinking, the relationship between the moments of the individual, the particular and the universal in them. Hegel himself showed differences in the relationship of these moments in concepts, judgments and conclusions; the forms of inference are determined both by the difference in the relations between these moments and by their content.

§ 3. The essence and content of Marxist dialectical logic

A brief consideration of the history of logic, the process of its division into two logics - formal and dialectical - creates the necessary prerequisites for the correct solution of the question of the subject of Marxist dialectical logic. As is known, heated debates have been taking place on this issue in our literature for a long time.

It seems that the discussion would more likely achieve its positive results if the disputing parties, when defining the subject of dialectical and formal logic, proceeded from objective foundations and tried to determine the objective facets that separate their subject. Often disputes occur around quotes, to which the disputants give different interpretations, bringing the content of the statements of great thinkers to their understanding of this subject. In this case, one’s subjective opinion is presented as an objective basis for determining the subject of a given science. Sometimes, as an objective basis for dividing the subject of formal and dialectical logic, the following criterion is put forward: in such and such a course of formal logic such and such a question is dealt with, which means it is included in the subject of formal, not dialectical logic. On this basis, they believe that the entire content of Aristotle’s logic and the logical teachings of F. Bacon should be included in formal logic, and everything that comes from Hegel should be included in dialectical logic. Further, when defining the subject of formal and dialectical logic, we must take into account the fact that the subject of logic, like any other science, changes. The subject of modern formal logic differs from the subject of the logic of Aristotle, Bacon, Kant, etc., and Marxist dialectical logic does not coincide with the logic of Hegel.

As the history of logic shows, the objective basis for dividing the subject of formal and dialectical logic can be the analysis of the cognitive process, its various sides. Any logic creates an apparatus for the functioning of thinking. If there is no such apparatus, then there is no logic. Therefore, it is legitimate to speak about materialist dialectics as logic only insofar as it creates such an apparatus, or rather an organism of thinking, which does not exist in any other logical system. What kind of device is this?

There is no clear answer to this question in Marxist literature. It seems to some that dialectics creates its own logic of inference from the premises of consequences, that is, its own logical calculus, built not on formal logical laws - identity, inadmissibility of contradiction, but on the laws of dialectics.

We cannot now analyze the forms of these calculi, since no one has yet succeeded in constructing them. What was proposed does not deserve serious attention. But this negative experience itself is very instructive and has undoubted significance in the development of logical thought. He once again proves that it is impossible to obtain logical calculus and at the same time discard the formal-logical law of the inadmissibility of contradiction.

Logical calculus is an apparatus for operating with signs according to given rules, among the latter some are mandatory for any calculus, others only for determining forms, among the former at least the formal-logical law of the inadmissibility of contradiction, violating it it is impossible to construct a single logical calculus.

But this does not mean that in principle it is impossible to make the laws of dialectics the rules of logical calculus. When operating with signs, we can, as a rule, include any meaningful statement, including the law of dialectics, but at the same time the minimum for the functioning of logical calculus must be preserved - the law of formal logic about the inadmissibility of contradiction in one or another formulation. Here the experience of the Russian logician N.A. Vasiliev is instructive, who attempted to build a system that he called non-Aristotelian, imaginary logic, in which he proceeds from the recognition of the existence of contradictions in the real world. But at the same time, as an absolute law for any logical system, he puts forward the law absolute discrimination truth and falsehood (“a judgment cannot be simultaneously true and false”), which in its content is identical to the formal-logical law of the inadmissibility of contradictions. As a result, N.A. Vasiliev obtained a new formalological system not with two (affirmative and negative), as in Aristotle, but with three types of judgments (another judgment of contradiction), with some additional modes of syllogism.

However, in principle, this was not a new dialectical logic, but simply the enrichment of the formal logical apparatus with new additions. N. A. Vasiliev included in his logical system statements that fix the unity of contradictory properties and relations in one subject, modern modal logic has gone even further in this regard, building a calculus with statements of possibility, impossibility, necessity, chance, and the so-called deontic logic distinguishes statements are obligatory, permitted, indifferent, prohibited. But no one calls modern modal logic with all its sections dialectical logic, since it functions as an apparatus of logical calculus, built according to the method of formal logic.

Materialistic dialectics is logic in a different sense than formal logic, and therefore, it creates a logical apparatus of a different nature, which does not function as a logical calculus. It takes thinking not as operating with signs according to certain rules (this is the task of formal logic), but as a process of creating concepts in which nature is given in a form transformed on the basis of human needs. Therefore, here we need an apparatus not for passing rules from sign to sign, but from concept to concept in the absence of these strict rules.

The task of materialist dialectics as a science includes: firstly, the discovery of the most general laws of development of the objective world and, secondly, the disclosure of their meaning as laws of thinking, their function in the movement of thinking. In the latter case, dialectics performs the functions of logic and becomes dialectical logic.

Dialectics as a science studies both objective and subjective dialectics; when it considers the laws of dialectics from their subjective side (as the laws of thinking), it acts as dialectical logic. Therefore, all laws and categories of dialectics are simultaneously laws of dialectical logic.

The laws and categories of materialist dialectics express the forms and patterns of nature, which have already entered the sphere human activity. And since, in principle, a person can make everything the subject of his work, he produces universally, hence the universality of the laws and categories of his thinking, which is capable of consciously operating with any object in accordance with its own form and measure, on the basis of an image that objectively correctly reflects this object.

A necessary prerequisite for the subject's practical mastery of an object is the achievement of knowledge of objective truth. In cognition, subject and object coincide theoretically, the object passes into the content of the cognitive image. The increase in the activity of the subject, its intrusion into the course of the objective process is an indispensable condition for complete, comprehensive reflection in the knowledge of the object as it exists independently of people’s consciousness.

Dialectical logic is the science of truth, the process of coincidence of the content of knowledge with an object, the categories in which thinking coincides and is consistent with objective reality. In other words, all logical categories, which in their connection and transitions make up the theory of dialectical logic, are universal definitions of reality, as it looks in objectively true thinking, tested and verified by human practice, since the definitions of “true” thinking are the definitions of correctly comprehended reality, and cannot be anything else. Logical categories are forms of agreement, coincidence (identity) of thought with reality.

The categories of dialectics appear simultaneously as forms of transition (transformation) of reality into thinking, into the form of knowledge, i.e. as a step of knowledge, reflection of the world in consciousness and as a step of transformation of knowledge into reality, as a step of practical implementation and verification of knowledge by practice.

The doctrine of truth and ways to achieve it is the main issue of dialectical logic. As the science of truth, dialectical logic first of all, it reveals the content of the philosophical method of cognition of truth, its basic requirements for how a person should approach the phenomena of the objective world, so that the result of cognition is a deep and comprehensive reflection in thinking of the essence of the subject. Based on knowledge of the most general patterns development of phenomena, dialectical logic forms methodological provisions that are the starting points in the study of any subject. It reveals the functions of the laws of dialectics in the knowledge of truth.

The basic requirements of dialectical logic in the study of a subject are formulated by V. I. Lenin as follows: “To really know a subject, one must embrace and study all its aspects, all connections and “mediations.” We will never achieve this completely, but the requirement of comprehensiveness will prevent us from making mistakes and from becoming dead. This is firstly. Secondly, dialectical logic requires that we take the subject in its development, “self-movement” (as Hegel sometimes says), change... Thirdly, all human practice must enter into the complete “definition” of the subject and how a criterion of truth and as a practical determinant of the connection of an object with what a person needs. Fourthly, dialectical logic teaches that “there is no abstract truth, truth is always concrete” 26.

Dialectical logic is not limited only to these requirements. From all the laws of dialectics and its categories certain requirements for thinking follow.

Dialectics is not some kind of canon, a testing authority for achieved knowledge, but an organon, a way and method of increasing real knowledge through a critical analysis of specific factual material, a method (method) of specific analysis of a real subject, real facts. But nevertheless, dialectical logic also performs a certain function in the process of proving theories.

The idea that one and the same philosophical method cannot be both a method and an achievement of new knowledge and its proof is characteristic of many trends in modern bourgeois philosophy. This idea ultimately comes from the recognition that the apparatus of formal logic, its laws and forms, is the only logical means of proof. No other science of proof, no other method of proof exists and cannot exist. Absolutization of the theory and method of proof developed by formal logic leads to metaphysics, to forgetting the role of dialectics in the process of proving scientific knowledge.

Of course, the importance of formal logic and its doctrine of proof cannot be underestimated; Marxist philosophy is not intended to replace formal logic in the doctrine of evidence, but to give what the latter cannot do. Modern positivists proceed from the fact that formal logic is a method of proof, and private methods are a method of discovering new results. Moreover, their method of proof and method of cognition are mutually exclusive. These particular methods act as a research method in the sciences, and formal logic acts as a method of proof, and no other general method of knowledge and proof exists. But such a division between the method of achieving new results and the method of proof is incorrect; it rests on a misunderstanding of the objective foundations of the method of proof and its connection with the movement towards truth.

Marxists at one time encountered critics of dialectics who separated and contrasted the method of research with the method of proof, reducing dialectics to a simple proof of known propositions. There were a lot of people who wanted to present dialectics, its laws and categories as a way of selecting facts, examples, and illustrations to prove some previously known position, both abroad and in Russia. They were exposed by Lenin in his work “What are “friends of the people” and how do they fight against the Social Democrats?” Already more than 80 years ago, Engels showed that even formal logic is not just a simple tool of proof, but is a method for obtaining new results.

This connection between the method of discovering truth and its proof is not accidental; it rests on the same idea of the coincidence in content of the laws of thinking with the laws of being. The process of proving the truth, as well as the process of discovering it, occurs according to the laws inherent in the objective world. The proof of truth is inextricably linked and is a subordinate moment in the process of achieving it. To prove the truth of any theoretical construction, it is necessary to reveal the path along which our thought went towards it, to analyze the factual material, the laws and methods of processing it, and the method of constructing the theory. The process of achieving truth cannot be depicted in this form: first it is discovered and then proven. The process of its discovery includes its proof, and, conversely, the proof of a theory is simultaneously its development, addition, and concretization.

Every scientific experiment contains this unity of discovering something new and proving or refuting any theoretical construct. It is incorrect to say that an experiment is only a tool for proving the truth of a theory or only a means of discovering new phenomena and constructing new hypotheses. By putting forward any new theoretical construction, we simultaneously refute something old and prove something new. The process of proof has no other goal than establishing objective truth and, conversely, achieving the latter includes proof as a moment. So, for example, in his work “Imperialism, as the highest stage of capitalism,” Lenin proves certain provisions that characterize the essence of imperialism. Proof of the truth of these provisions is Lenin’s real way of researching new phenomena characteristic of imperialism, generalizing them on the basis of Marxist philosophy, which in this case acts as both a research method and, along with formal logic, a method of proof.

Formal logic is limited as a method of cognition, and it is also limited as a tool of proof. On the basis of its laws and forms, it is possible to establish the correspondence or inconsistency of one judgment with another judgment, that is, formal logic serves as a tool for proving the correctness of judgments, but not their objective truth. As the science of evidence, formal logic develops criteria by which one can judge: whether or not any judgment necessarily follows from a system of other judgments. These criteria are important in constructing a theory and proving it. If a theory includes such logical contradictions that, according to the laws of formal logic, are unacceptable, then it cannot claim to be objectively true and scientific. But fulfilling all the requirements of formal logic cannot serve as proof of the objective truth of a theoretical construction. Therefore, the logical apparatus of formal logic, as a tool of proof, performs only one necessary function - it tests scientific knowledge in terms of its formal correctness and rigor.

Marxist philosophy, its logical arsenal serves as a tool for proving the objective truth of knowledge. She developed a method for discovering truth and proving it, considering the establishment of formal correctness only as a moment in the movement towards truth and in its proof.

Consideration of an object in its self-movement, with all its connections, is not only the way to achieve the truth, but also its proof. Special meaning evidence has practice, without which it is generally impossible to resolve the question of the truth or falsity of any theoretical construction. The unity of theory and practice is the most important methodological position of Marxist philosophy, serving as a guiding principle in the study of the subject and in establishing the truth of the acquired knowledge. As is known, a scientific position is considered proven if it is logically deduced from other provisions, the truth of which was previously established. But it is impossible to resolve the question of the truth of any scientific position that serves as an argument in proof, nor the correctness of the logical deduction itself, unless one goes beyond thinking into the area of practical activity. Is the content of our thinking objective, are we dealing with the own properties of the object, or has thinking fallen into an illusion, moving in the area of subjective ideas, divorced from the comprehended properties, patterns inherent in the objective world? There is no answer to this question if we ignore the role of practice in proving truth.

How the doctrine of the method of achieving and proving truth, dialectical logic It has their approaches to forms of thinking, the study of which has always been the subject of logic. In the study forms of thinking it comes primarily from materialistic solution to the fundamental question of philosophy. Defining the main content of dialectical logic as a science, V. I. Lenin wrote: “ The totality of all sides of the phenomenon, reality and them (mutually) relationship- this is what the truth is made of. Relations (= transitions = contradictions) of concepts are the main content of logic, and these concepts (and their relationships, transitions, contradictions) are shown as reflections of the objective world. Dialectics of things creates dialectic ideas, and not vice versa" 27.

Marxism considers the logical (the movement of thinking) as a reflection of the historical (the movement of phenomena of objective reality). To reflect fully and deeply objective dialectics, the forms of thinking themselves must be dialectical - mobile, flexible, interconnected. Dialectics studies the connection between forms of thinking, their subordination in the process of the movement of knowledge towards truth. “Dialectical logic,” writes F. Engels, “in contrast to the old, purely formal logic, is not content with listing and without any connection placing next to each other forms of movement in thinking, that is, various forms of judgments and inferences. On the contrary, it derives these forms from one another, establishes between them a relationship of subordination, not coordination, it develops higher forms from lower ones” 28.

The solution to this problem is based on dialectical logic based on the principle of the unity of the abstract and the concrete in scientific and theoretical thinking, the movement of thinking from the abstract to the concrete is a way to achieve true objectivity in knowledge. The principle of the unity of the abstract and the concrete occupies a special place in dialectical logic; the construction of the entire system of dialectical logic is based on it: the development of judgments, concepts, conclusions, scientific theories, hypotheses is nothing more than a process of ascension from the abstract to the concrete.

Finally, dialectical logic analyzes the structure of forms of thinking, focusing on the dialectic of the relationship between the individual, the particular and the universal in them as a reflection of the relations of the objective world.

Thus, dialectical logic is the science of truth and ways to achieve it, it reveals the laws and forms of development of thinking along the path of achieving truth, its logical apparatus is the laws and categories of dialectics.

Notes:

1 V. I. Lenin. Complete collection works, vol. 29, p. 156.

2 Collection of minutes of meetings of sections of physics and mathematics. Sciences of the Society of Natural Scientists at Kazan University, Kazan, 1884, p. 1.

3 A. Church. Introduction to mathematical logic. T. 1. M., 1960. p. 49

4 J. Lukasiewicz. Aristotelian syllogistic from the point of view of owls

belt formal logic. M., 1959, p. 48.

5 Ibid., p. 52

6 L. L. Markov. Mathematical logic. - “Philosophical Encyclopedia”, vol. 3, p. 340.

7 A. A. Zinoviev. Fundamentals of the logical theory of scientific knowledge. M., 1967. p. 4.

9 V. I. Lenin. Complete Works, vol. 18, p. 364.

10 K. Marx and F. Engels. Works, vol. 20, p. 138.

11 V. I. Lenin. Complete Works, vol. 42, pp. 289-290.

12 V. I. Lenin. Complete Works, vol. 29, p. 326.

13 Thus, in “Discourse on Method” R. Descartes wrote: “In his youth from philosophical sciences I studied logic a little, and from mathematics - geometric analysis and algebra - three arts or sciences that, it would seem, should give something to the realization of my intention. But, studying them, I noticed that in logic its syllogisms and most of its other instructions quickly help to explain to others what we know, or even, as in the art of Lull, to reason stupidly about what you do not know, instead of studying This. And although logic indeed contains many very correct and good prescriptions, they are, however, mixed with so many others - either harmful or unnecessary - that it is almost as difficult to separate them as to discern Diana or Minerva in an unfinished block of marble. (R. Descartes. Selected works. M., 1950, p. 271).

14 Kant himself defines the subject of formal logic as follows: “The boundaries of logic are absolutely precisely determined by the fact that it is a science that thoroughly expounds and strictly proves only the formal rules of all thinking (it makes no difference whether it is a priori or empirical, it makes no difference what its origin and subject matter are). and whether it encounters random or natural obstacles in our soul)” (I. Kant. Works, vol. 3, p. 83).

15 I. Kant. Works, vol. 3, p. 159.

17 V. F. Asmus. Kant's dialectics. M., 1930, p. 57.

18 This feature of Kant’s logic was pointed out by Hegel when he wrote: “Different types of judgments must be understood not only as empirical diversity, but also as a certain integrity determined by thinking. One of Kant's great merits is that he first put forward this requirement. Although Kant’s division of judgments into judgments of quality, quantity, relation and modality, according to the scheme of his table of categories, cannot be considered satisfactory, partly due to the purely formal application of the scheme of these categories, partly also because of their content, however, the basis of this division nevertheless lies the true view, the understanding that the various types of judgment are determined precisely by the universal forms of the logical idea itself” (Hegel. Works, vol. I, pp. 277-278). We believe that the assessment of Kant’s classification given in the article by M. N. Alekseev “On the dialectical nature of judgment.” (“Questions of Philosophy”, 1956, No. 2, p. 60), is incorrect. M. Alekseev believes that Kant did not try to introduce anything new into the classification of judgments, that it was built on the principle of pure coordination and does not represent anything original. Although M. Alekseev refers to Hegel, it is already clear from the above statement that Hegel approached the assessment of Kant’s logical theory more subtly and deeply.

19 “Mere consideration of these forms,” writes Hegel, “as knowledge of the various forms and turns of this activity, is already quite important and interesting. For no matter how dry and meaningless the enumeration of various types of judgments and inferences and their varied interweavings may seem to us, no matter how unsuitable they may seem to us for finding the truth, we still cannot put forward any other science in contrast to this. If it is considered a worthy endeavor to know the countless number of animals, to know one hundred and sixty-seven species of cuckoos, of which one has a different crest on its head than another; if it is considered important to learn about a new pathetic species of the family of the pathetic genus lichen, which is no better than a scab, or if the discovery of a new species of some insect, reptiles, bedbugs, etc. is considered important in scientific works on entomology, then it must be said that it is important get acquainted with various types of movement of thought than with these insects” (Hegel. Works, vol. X, M., 1932, p. 313).

20 See Hegel. Works, vol. I, page 66.

21 See Hegel. Works, vol. X, page 316.

22 “...Definitions of inference,” writes Hegel, “are placed here on a par with combinations of dice or cards in the game of ombre; the rational is taken as something lifeless and alien to the concept...” (Hegel, Works, vol. VI, p. 132). Speaking about Pluquet’s logical calculus, Hegel notes that it “...represents, of course, the worst that can be said about any invention in the field of presentation of logical science” (ibid., p. 133). Hegel approached logical calculus from only one side: what it can provide for the philosophical interpretation of the essence of thinking, in particular, concepts, judgments and inferences. He is, of course, right in the sense that in logical calculus the content of the logical forms themselves becomes impoverished. However, he did not see and did not understand that in logical calculus, formal logic in the study of forms of thinking goes beyond the boundaries of philosophy, approaching them from a purely special, non-philosophical side.

23 Hegel. Essay, vol. VI, p. 27.

24 Hegel. Essay, vol. X, p. 314.

26 V. I. Lenin. Complete Works, vol. 42, p. 290.

27 V. I. Lenin. Complete Works, vol. 29, p. 178.

28 K. Marx and F. Engels. Works, vol. 20, p. 538.