Logical forms of thinking. Logical thinking and its forms

The main forms of abstract (logical) thinking are concept, judgment, inference

Each of these logical forms will be the subject of our study in the following sections. We will now briefly look at them in order to illuminate the concept of logical form

Individual objects or their combinations are reflected by our thinking in concepts that are different in content. For example, “textbook” and “crime” are concepts that reflect completely different objects of thought. A textbook is a printed source of knowledge about the basics of a science and serves to train future specialists. A crime is a socially dangerous, illegal, guilty and punishable act. As we see, these different objects appear in thinking in the same way - as a certain set of their common, essential properties and recognizable powers and signs.

By highlighting the characteristic features of one object, or the repeating and general features of a certain set of objects, we form the concept of an object “A” as a certain set of its essential features “a”, “b”, “c”

Thus, various objects are reflected in human thinking in the same way - as a certain connection of their essential features, i.e. in the form of a concept

The form of judgment reflects the relationship between objects and their properties. These relationships are affirmed or denied. For example, “the accused has the right to defense” and “The Volga does not flow into the Black Sea but into the Black Sea.”

The above judgments are different in their content, but the way of connecting the components of their content is the same - this connection is expressed in the form of affirmation or negation. Having denoted the concepts included in the judgment, accept the symbols accepted in logic S (subject - from Latin - the one that lies below is at the basis of the concept of the subject of the judgment) - this is how the concept of the subject of the judgment is denoted - and. P (predicate - from Latin - said, a sign of an object) - the concept of a sign of an object, we get a scheme that is common for any judgment of this type: "S -. P", where S and. P-concepts included in the judgment, and the sign “-” means the connection between them. In S and. P can be understood as any objects and their properties, under the sign "-" - any connection (affirmative, negative, affirmative, and transverse).

Thus, a judgment is a certain way of displaying the relations of objects of reality, which is expressed in the form of a statement or in the form of a negation

Considering an inference with the help of which a new judgment is derived from one or more judgments, we can establish that in inferences of the same type the conclusion is carried out in the same way

For example:

All philologists study logic

We are philology students

We study logic

The conclusion (“We study logic”) is necessarily deduced from the premises in that they are connected by the common concept of “philologists”

In the same way, that is, thanks to the meaningful connection between judgments and premises, it is possible to obtain a conclusion from any judgments with different contents

So, we highlight something common in inferences with different contents: the method of connection between judgments

Having examined the basic forms of thinking - concepts, judgments and inferences, we found in them something in common that does not depend on the substantive content of thoughts, namely: the way of connecting the elements of thought - features in a concept and concepts in a judgment and judgments in an inference. Due to these connections, the content of thoughts does not exist on its own, but in certain logical forms: concepts, judgments, conclusions.

Logical form or form of thinking is a way of connecting the elements of thought, its structure, thanks to which the content exists and reflects reality

In the real process of thinking, the content and form of thought exist in inextricable unity. There is no content that is devoid of form, just as there is no form that is meaningless. But for the purpose of special analysis, we abstract from the substantive content of thoughts and focus on studying their form. Logical forms are outside their specific content and is the most important task of the science of logic.

This is the general concept of logical form

Unlike others, it is performed in accordance with a certain logic.

In the structure of thinking, the following logical operations can be distinguished:

• comparison;
• analysis;
• synthesis;
• abstraction;
• generalization.

Comparison- mental operations based on

Analysis- a mental operation of dividing a complex object into its constituent parts or characteristics and then comparing them.

Synthesis- an operation opposite to analysis, allowing Analysis and synthesis are usually carried out together, contributing to a deeper knowledge of reality.

Abstraction — highlighting the essential properties and connections of an object and abstracting from others, insignificant.

Generalization- mental association of objects and phenomena according to their common and essential characteristics.

Forms of logical thinking

The main forms of logical thinking are:

• concepts;
• judgments;
• inferences.

Concept

Concept - form of thinking that reflects in a word concrete and abstract.

Judgment

Judgment - form of thinking that reflects communications approval form or denial.

Inference

Conclusion - conclusion.

The conclusions differ:

• inductive;
• deductive;
• Similarly.

Induction- logical conclusion in the process of thinking from the particular to the general.

Deduction- logical conclusion in the process of thinking from the general to the specific.

Analogy- logical conclusion in the process of thinking from private to private

Emotions can not only distort, but also stimulate thinking. It is known that feeling will give tension, sharpness, purposefulness and perseverance to thinking. According to , without sublime feelings, productive thought is just as impossible as without logic, skills, and abilities.

Logic and emotions in the thinking process

Unlike other processes, it is carried out in accordance with a certain logic. In the structure of thinking, the following logical operations can be distinguished: comparison, analysis, synthesis. abstraction and generalization.

Comparison - mental operation based on establishing similarities and differences between objects. The result of the comparison can be a classification, which acts as the primary form of theoretical knowledge.

Analysis is a mental operation of dividing a complex object into its constituent parts or characteristics and then comparing them.

Synthesis - an operation inverse to analysis that allows mentally recreate a whole from analytically given parts. Analysis and synthesis are usually carried out together, contributing to a deeper Knowledge of reality.

Abstraction - mental operation based on you divide the essential properties and connections of an object and abstract from others, insignificant. These highlighted characteristics do not actually exist as independent objects. Abstraction facilitates a more thorough study of them. The result of abstraction is the formation of concepts.

Generalization is a mental unification of objects and phenomena according to their common and essential characteristics.

Basic forms of logical thinking are concepts, judgments and inferences.

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

Judgment - form of thinking that reflects communications between objects and phenomena in approval form or denial. Propositions can be true or false.

Conclusion - a form of thinking in which, based on several judgments, a certain one is made conclusion. Inferences are distinguished between inductive, deductive and analogical.

Induction is a logical conclusion in the process of thinking from the particular to the general. Deduction is a logical conclusion in the process of thinking from the general to the specific.

Analogy - logical conclusion in the process of thinking from private to private based on some similarities.

Although thinking is carried out on the basis of logical operations, it does not always act as a process in which only logic and reason act. Emotions very often interfere with the thinking process, changing it. Emotions subordinate thought to feeling, forcing one to select arguments that speak in favor of the desired decision.

Emotions can not only distort, but also stimulate thinking. It is known that feeling gives tension, sharpness, purposefulness and persistence to thinking. According to psychology, without sublime feelings, productive thought is just as impossible as without logic, knowledge, skills.

1. Subject of logic. Basic logical forms.

Logic comes from the Greek. logos, which simultaneously means speech, word, statement, concept. The founder of logic, Aristotle, most often used the term “logos” in the sense of “definition” or “reasonableness in general.”

So, in the modern understanding, logic is the science of the laws and forms of correct thinking.

Form of thinking - this is a way of connecting the elements of thought. Basic forms of thinking (logical forms): concept, judgment, inference.

Concept is the original, simplest form of thought, reflecting the general essential characteristics of objects.

Judgment- this is a form of thinking in which the connection between an object and its attribute is affirmed or denied. It has the property of expressing either the truth (correspondence to reality) or a lie.

Inference- the most complex form of thought, represents the receipt of a new judgment (conclusion) from given judgments (premises).

Logic, as a separate science, was first systematically expounded by the ancient Greek philosopher Aristotle (384 - 322 BC). Aristotle formulated the basic laws of correct thinking: law of identity, law of non-contradiction, law of excluded middle. Later the fourth law was formulated - law of sufficient reason. The development of logic was largely due to social need. A citizen of the ancient polis actively participated in public life. A freeborn man must have held an important government position at least once in his life. This required some preparation. Therefore, the so-called “teachers of wisdom” - the sophists - were highly valued. They taught literacy, eloquence, the art of argument, etc., but over time they began to invent techniques for fooling their interlocutor. Such dishonest methods were called “sophisms,” and the word “sophist” acquired a negative meaning.

Here are examples of some sophisms that have become classics:

“What you haven’t lost, you have. You didn’t lose your horns. That means you have them (you’re horned)”;
“He who is sitting has stood up. He who has stood up is standing. This means that he who is sitting is standing”;
“I am a person. You are not me. That means you are not a person”;
“Medicine for a sick person is good. The more good, the better. So the more medicine you give to a sick person, the better.”

Here are some sophistic questions:

"Have you stopped hitting your mother?";
"How long have you been out of prison?" and so on.

Obviously, any answer to such a question will not suit you. When getting involved, for example, in such a dispute, “I bet I lifted the tractor?” you doom yourself to losing in advance (“I picked it up, but didn’t pick it up” or “I picked it up, but it was a toy”). Just like answering questions like this:

"- Do you know what I want to ask you now? - No, we don’t know. - Don’t you know that lying is wrong? - We know. - But that’s exactly what I was going to ask you about, and you answered that "You don't know. It turns out you know what you don't know!"

The ambiguity of many linguistic expressions, hidden statements in questions, all this allows sophistry to look convincing to an unprepared person. The ability to use sophisms presupposes knowledge of the basics of logic.

It was precisely as a means of defense against sophistry and lies that logic was conceived by Aristotle. Subsequently, medieval scholastics made a significant contribution to the development of logic (they introduced Latin terminology). The English philosopher F. Bacon (1561-1626) laid the foundations of the doctrine of inductive inferences. The German philosopher Leibniz (1646-1716) formulated the law of sufficient reason. In the middle of the 19th century. mathematical (symbolic) logic arose. Since then, Aristotelian logic began to be called traditional (formal) logic.

2. Laws of logic.

3. The meaning of logic.

The achievements of formal logic are used in law, psychology, linguistics, management theory, pedagogy and other sciences. Some branches of logic are the theoretical basis of mathematics, information theory, and cybernetics.

When studying logic one develops:

1. accurate thinking and clear speech;
2. the ability to persuade and justify your ideas;
3. ability to argue;
4. the habit of analyzing our own and others’ reasoning, which helps us cope with sophistry and lies.

But still, the main significance of logic is that it teaches one to think and strengthens a person’s thinking abilities.

Investigator - investigator of the prosecutor's office

The Constitution is the law

Society is a person

Poetic meter – Iambic meter

6. Three examples of deductive reasoning:

If the day is sunny, the pine forest smells of resin.
The day is sunny.
____________________
Consequently, the pine forest smells of resin.

2. All stars emit energy

The sun is a star.

_________________________________________________
Therefore, the Sun emits energy.

3. If the court decision is appealed, then it has not yet entered into legal force.
The court's decision was appealed.
_____________________________________________
Therefore, it has not yet entered into legal force.

Thinking- this is the process of indirect and generalized reflection, establishing existing connections and relationships between objects and phenomena of reality.

Thinking- a cognitive process of a higher level compared to the direct sensory reflection of reality in sensations, perceptions, and ideas. Sensory knowledge provides only an external picture of the world, while thinking leads to knowledge of the laws of nature and social life.

Thinking performs a regulatory, cognitive and communicative function, i.e., a communication function. And here its expression in speech acquires special significance. Whether thoughts are transmitted orally or in writing in the process of communication between people, whether a scientific book or a work of fiction is written - everywhere the thought must be formalized in words so that other people understand it.

Sensory reflection and thinking- a unified process of human cognition of the surrounding reality. The source of knowledge is practice. It all begins with sensations and perceptions, that is, with living contemplation. In no other way can one obtain knowledge about various objects and phenomena, about the properties of things, about various forms of movement of matter. Only then does sensory knowledge ascend to mental - abstract, logical. But even at the level of abstract thinking, its connection with sensory images of sensations, perceptions and ideas remains.

Such abstract and generalized knowledge allows us to understand the world more fully and deeply. The truth of such knowledge is verified by practice. Here it already acts as a criterion for the correctness of human cognition, human thinking. The unity of sensory reflection and thinking allows us to compare the past and present, to foresee and project the future. This applies not only to the surrounding world of things, phenomena, other people, but also to the person himself, allowing him to “learn to control himself.”

Like all mental phenomena, thinking is a product of reflex activity of the brain. The unity of the sensory and logical in thinking is based on the complex interaction of the cortex and subcortical formations of the brain.

Thinking - always solving some problem, searching for an answer to a question that has arisen, searching for a way out of the current situation. At the same time, no solution, no answer, no way out can be seen only by perceiving reality.

Thinking - it is not only an indirect, but also a generalized reflection of reality. Its generality lies in the fact that for each group of homogeneous objects and phenomena, common and essential features that characterize them are identified. As a result, knowledge about this object in general is formed: a table in general, a chair in general, a tree in general, etc. The essential features of “man in general,” for example, are the following general features: man is a social being, a worker, who has speech. To highlight these general and essential features, you need to abstract yourself from private, unimportant features, such as gender, age, race, etc.

Distinguish visual-effective, visual-figurative and verbal-logical thinking.

Visual-effective thinking. It is also called practically effective or simply practical thinking. It occurs directly in the process of people’s practical activities and is associated with the solution of practical problems: production, organization of the educational process. This type of thinking is, one might say, fundamental throughout a person’s life.

Visual-figurative thinking. This type of thinking is associated with solving mental problems based on figurative material. Here we operate with a wide variety of images, but most of all with visual and auditory images. Visual-figurative thinking is closely related to practical thinking.

Verbal and logical thinking. It is also called abstract or theoretical. It has the form of abstract concepts and judgments and is associated with the operation of philosophical, mathematical, physical and other concepts and judgments. This is the highest level of thinking, allowing one to penetrate into the essence of phenomena and establish the laws of development of nature and social life.

All types of thinking are closely interconnected. However, for different people one or another species occupies a leading position. Which one is determined by the conditions and requirements of the activity. For example, a theoretical physicist or a philosopher has verbal-logical thinking, while an artist has visual-figurative thinking.

The relationship between types of thinking is also characterized by their mutual transitions. They depend on the tasks of activity, requiring first one, then the other, or even joint manifestation of types of thinking.

Basic logical forms of thinking- concept, judgment, inference.

Concept- this is a thought expressed in a word about the general and essential characteristics of objects and phenomena of reality. In this way it differs from representations that only show their images. Concepts are formed in the process of historical development of mankind. Therefore, their content acquires the character of universality. This means that even though the same concept is denoted differently by words in different languages, the essence remains the same.

Concepts are mastered in the process of a person’s individual life as he enriches himself with knowledge. The ability to think is always associated with the ability to operate with concepts, to operate with knowledge.

Judgment- a form of thinking in which the affirmation or denial of certain connections and relationships between objects, phenomena and events is expressed. Judgments can be general (for example, “all plants have roots”), particular, or single.

Inference- a form of thinking in which a new judgment is derived from one or more judgments, one way or another completing the thought process. There are two main types of inferences: inductive (induction) and deductive (deduction).

Inference is called inductive. from particular cases, from particular judgments to the general. For example: “when Ivanova turned 14 years old, she received a Russian citizen passport,” “when Rybnikov turned 14 years old, he received a Russian citizen passport,” etc. Consequently, “all Russians who have reached the age of 14 receive a Russian citizen passport "

There is also a conclusion by analogy. It is usually used to build hypotheses, i.e., assumptions about the possibility of certain events and phenomena.

The process of inference thus, it is the operation of concepts and judgments, leading to one or another conclusion.

Mental operations are called mental actions used in the process of thinking. These are analysis and synthesis, comparison, generalization, abstraction, specification and classification.

Analysis- mental division of the whole into parts, highlighting individual signs and properties.

Synthesis- mental connection of parts, features, properties into a single whole, mental connection of objects, phenomena, events into systems, complexes, etc.

Analysis and synthesis are interconnected m. The leading role of one or the other is determined by the tasks of the activity.

Comparison- mental establishment of similarities and differences between objects and phenomena or their signs.

Generalization- mental unification of objects or phenomena based on selection when comparing common and essential properties and characteristics for them.

Abstraction- mental distraction from any properties or signs of objects, phenomena.

Specification- mental selection from the general of one or another particular specific property and feature.

Classification- mental separation and subsequent unification of objects, phenomena, events into groups and subgroups according to certain characteristics.

Mental operations, as a rule, do not occur in isolation, but in various combinations.

Analysis and synthesis form a unity. In the process of analysis, a comparison takes place in order to identify common and different characteristics of a particular group of phenomena or objects.

Thinking, as is known, - generalized reflection of reality. The process of identifying common essential features requires abstraction, therefore, abstraction is also included in the process of analysis and synthesis.

Thinking can be figurative- at the level of images, perceptions and ideas. It also exists to some extent in higher animals. Human higher thinking is verbal thinking. Language, speech is the material shell of thought. Only in speech - oral or written form - does a person’s thought become accessible to others.

Individual characteristics of thinking manifest themselves in various properties of mental activity. They develop in the process of life and activity and are largely determined by the conditions of training and upbringing. Typological features of higher nervous activity are also important.

Among the features of thinking include breadth and depth of mind, consistency, flexibility, independence and critical thinking.

Breadth of mind characterized by versatility of knowledge, the ability to think creatively, the ability to make broad generalizations, and the ability to connect theory with practice.

Depth of mind- this is the ability to isolate a complex issue, delve into its essence, separate the main from the secondary, foresee the paths and consequences of its solution, consider the phenomenon comprehensively, understand it in all connections and relationships.

Sequence of thinking is expressed in the ability to establish a logical order in solving various issues.

Flexibility of thinking- this is the ability to quickly assess a situation, quickly think and make the necessary decisions, and easily switch from one method of action to another.

Independence of thinking is expressed in the ability to pose a new question, find an answer to it, make decisions and act in a non-standard way, without succumbing to suggestive outside influences.

Critical thinking characterized by the ability not to consider the first thought that comes to mind to be correct, to subject the proposals and judgments of others to critical consideration, to make the necessary decisions only after weighing all the pros and cons.

The listed features of thinking are combined differently in different people and expressed to varying degrees. This characterizes the individual characteristics of their thinking.

Conditions for the development of thinking in the educational process.

When studying the development of a child's thinking, it is always necessary to take into account the main difference between the conditions of phylogenetic and ontogenetic development. Along the line of phylogenetic development, the stimulus for thinking has always mainly been needs, the satisfaction of which had more or less pronounced vital significance; here thinking arose and developed on the basis of serious activity - service and, especially, labor. As for ontogenesis - especially within childhood, the situation here is different. Childhood is the period of a person’s life when he himself does not have to worry about meeting his basic needs - this is done by others, his educators, and adults. A person ceases to be considered a child only after he becomes forced to take care of satisfying his life needs, that is, to solve the problems facing him with his own strength.

Therefore, during childhood, the impulse for the development of thinking is the need to satisfy not the needs of life, as is the case in phylogenesis, but the needs of another category, in particular, the needs development. The development of children's thinking occurs mainly on the basis of games And study. Taking this circumstance into account is not only of great theoretical, but perhaps even greater practical importance, since when educating thinking, knowledge of where the child’s thinking impulses come from is certainly of fundamental importance

The development of thinking as an activity occurs in communication, in actions with objects, in play, and in didactic classes. The accumulation of experience in activity and its generalization in the form of various targeted ways of acting with objects, ways of communicating with people ensures the correct development of the child’s thinking and its transformation from visual-effective at an early age to visual-figurative and conceptual at preschool and school age.

Every day we are faced with many tasks, the solution of which requires our ability to think logically. Logic as the ability to think and reason consistently and consistently is required in many life situations, from solving complex technical and business problems to persuading interlocutors and making purchases in a store.

But despite the high need for this skill, we often make logical mistakes without knowing it. Indeed, among many people there is an opinion that it is possible to think correctly on the basis of life experience and so-called common sense, without using the laws and special techniques of “formal logic”. To perform simple logical operations, express elementary judgments and simple conclusions, common sense can also be suitable, but if we need to understand or explain something more complex, then common sense often leads us to errors.

The reasons for these misconceptions lie in the principles of development and formation of the foundations of logical thinking in people, which are laid in childhood. Teaching logical thinking is not carried out purposefully, but is identified with mathematics lessons (for children at school or for students at the university), as well as with solving and passing a variety of games, tests, tasks and puzzles. But such actions contribute to the development of only a small proportion of logical thinking processes. In addition, they explain to us the principles of finding solutions to tasks in a rather primitive way. As for the development of verbal-logical thinking (or verbal-logical), the ability to correctly perform mental operations, consistently come to conclusions, for some reason we are not taught this. That is why the level of development of people's logical thinking is not high enough.

We believe that a person’s logical thinking and his ability to cognition should develop systematically and on the basis of a special terminological apparatus and logical tools. During the classes of this online training, you will learn about self-education methods for the development of logical thinking, get acquainted with the main categories, principles, features and laws of logic, and also find examples and exercises for applying the acquired knowledge and skills.

What is logical thinking?

To explain what “logical thinking” is, let’s divide this concept into two parts: thinking and logic. Now let's define each of these components.

Human thinking- this is the mental process of processing information and establishing connections between objects, their properties or phenomena of the surrounding world. Thinking allows a person to find connections between the phenomena of reality, but in order for the connections found to truly reflect the true state of affairs, thinking must be objective, correct or, in other words, logical, that is, subject to the laws of logic.

Logics translated from Greek has several meanings: “the science of correct thinking”, “the art of reasoning”, “speech”, “reasoning” and even “thought”. In our case, we will proceed from the most popular definition of logic as a normative science about the forms, methods and laws of human intellectual mental activity. Logic studies ways to achieve truth in the process of cognition in an indirect way, not from sensory experience, but from knowledge acquired earlier, therefore it can also be defined as the science of ways to obtain inferential knowledge. One of the main tasks of logic is to determine how to come to a conclusion from existing premises and gain true knowledge about the subject of thought in order to better understand the nuances of the subject of thought being studied and its relationships with other aspects of the phenomenon under consideration.

Now we can define logical thinking itself.

This is a thought process in which a person uses logical concepts and constructions, which is characterized by evidence, prudence, and the goal of which is to obtain a reasonable conclusion from existing premises.

There are also several types of logical thinking; we list them, starting with the simplest:

Figurative-logical thinking

Figurative-logical thinking (visual-figurative thinking) - various thought processes of the so-called “imaginative” problem solving, which involves a visual representation of the situation and operating with images of its constituent objects. Visual-figurative thinking, in fact, is synonymous with the word “imagination”, which allows us to most vividly and clearly recreate the whole variety of different actual characteristics of an object or phenomenon. This type of human mental activity is formed in childhood, starting from approximately 1.5 years.

To understand how developed this type of thinking is in you, we suggest you take the IQ Test “Raven’s Progressive Matrices”

The Raven's Test is a progressive matrix scale for assessing IQ, mental ability, and logical thinking, developed in 1936 by John Raven and Roger Penrose. This test can give the most objective assessment of the IQ of the people being tested, regardless of their level of education, social class, type of activity, linguistic and cultural characteristics. That is, it can be said with a high probability that the data obtained as a result of this test from two people from different parts of the world will evaluate their IQ equally. The objectivity of the assessment is ensured by the fact that this test is based solely on images of figures, and since Raven's matrices are among non-verbal intelligence tests, its tasks do not contain text.

The test consists of 60 tables. You will be offered drawings with figures connected to each other by a certain relationship. One figure is missing; it is given at the bottom of the picture among 6-8 other figures. Your task is to establish a pattern that connects the figures in the picture and indicate the number of the correct figure by choosing from the proposed options. Each series of tables contains tasks of increasing difficulty, while at the same time, the complication of the type of tasks is observed from series to series.

Abstract logical thinking

Abstract logical thinking- this is the completion of a thought process with the help of categories that do not exist in nature (abstractions). Abstract thinking helps a person model relationships not only between real objects, but also between abstract and figurative ideas that thinking itself has created. Abstract logical thinking has several forms: concept, judgment and inference, which you can learn more about in the lessons of our training.

Verbal and logical thinking

Verbal and logical thinking (verbal-logical thinking) is one of the types of logical thinking, characterized by the use of linguistic means and speech structures. This type of thinking requires not only the skillful use of thought processes, but also competent command of one’s speech. We need verbal-logical thinking for public speaking, writing texts, arguing, and in other situations where we have to express our thoughts using language.

Applying logic

Thinking using the tools of logic is necessary in almost any area of ​​human activity, including the exact sciences and humanities, economics and business, rhetoric and public speaking, the creative process and invention. In some cases, strict and formalized logic is used, for example, in mathematics, philosophy, and technology. In other cases, logic only provides a person with useful techniques for obtaining a reasonable conclusion, for example, in economics, history, or simply in ordinary “life” situations.

As already mentioned, we often try to think logically on an intuitive level. Some people do it well, some do it worse. But when connecting the logical apparatus, it is better to know exactly what mental techniques we use, since in this case we can:

• More precisely, choose the right method that will allow you to come to the right conclusion;
• Think faster and better - as a consequence of the previous point;
• It is better to express your thoughts;
• Avoid self-deception and logical fallacies,
• Identify and eliminate errors in other people’s conclusions, cope with sophistry and demagoguery;
• Use the necessary argumentation to convince your interlocutors.

The use of logical thinking is often associated with quickly solving logic tasks and passing tests to determine the level of intellectual development (IQ). But this direction is associated to a greater extent with bringing mental operations to automatism, which is a very insignificant part of how logic can be useful to a person.

The ability to think logically combines many skills in the use of various mental actions and includes:

1. Knowledge of the theoretical foundations of logic.
2. The ability to correctly perform such mental operations as: classification, specification, generalization, comparison, analogy and others.
3. Confident use of key forms of thinking: concept, judgment, inference.
4. The ability to argue your thoughts in accordance with the laws of logic.
5. The ability to quickly and effectively solve complex logical problems (both educational and applied).

Of course, such operations of thinking using logic as definition, classification and categorization, proof, refutation, inference, conclusion and many others are used by every person in his mental activity. But we use them unconsciously and often with errors, without a clear idea of ​​the depth and complexity of those mental actions that make up even the most elementary act of thinking. And if you want your logical thinking to be truly correct and rigorous, you need to learn this specifically and purposefully.

How to learn this?

Logical thinking is not given to us from birth, it can only be learned. There are two main aspects of teaching logic: theoretical and practical.

Theoretical logic , which is taught at universities, introduces students to the basic categories, laws and rules of logic.

Practical training aimed at applying the acquired knowledge in life. However, in reality, modern teaching of practical logic is usually associated with passing various tests and solving problems to test the level of intelligence development (IQ) and for some reason does not address the application of logic in real life situations.

To truly master logic, you need to combine theoretical and applied aspects. Lessons and exercises should be aimed at developing intuitive, automated logical tools and consolidating the acquired knowledge in order to apply it in real situations.

Based on this principle, the online training that you are reading now was compiled. The purpose of this course is to teach you to think logically and apply logical thinking methods. Classes are aimed at introducing the basics of logical thinking (thesaurus, theories, methods, models), mental operations and forms of thinking, rules of argumentation and laws of logic. In addition, each lesson contains tasks and exercises to train you to use the acquired knowledge in practice.

Logic lessons

Having collected a wide range of theoretical materials, as well as having studied and adapted the experience of teaching applied forms of logical thinking, we have prepared a series of lessons for the full mastery of this skill.

We will devote the first lesson of our course to a complex but very important topic - the logical analysis of language. It’s worth mentioning right away that this topic may seem abstract to many, loaded with terminology, and inapplicable in practice. Don't be scared! Logical analysis of language is the basis of any logical system and correct reasoning. The terms that we learn here will become our logical alphabet, without knowledge of which we simply cannot go further, but gradually we will learn to use it with ease.

A logical concept is a form of thinking that reflects objects and phenomena in their essential features. Concepts come in different types: concrete and abstract, individual and general, collective and non-collective, irrespective and correlative, positive and negative, and others. Within the framework of logical thinking, it is important to be able to distinguish these types of concepts, as well as produce new concepts and definitions, find relationships between concepts and perform special actions on them: generalization, limitation and division. You will learn all this in this lesson.

In the first two lessons we said that the task of logic is to help us move from an intuitive use of language, accompanied by errors and disagreements, to a more orderly use of it, devoid of ambiguity. The ability to handle concepts correctly is one of the skills required for this. Another equally important skill is the ability to correctly define. In this lesson we will tell you how to learn this and how to avoid the most common mistakes.

Logical judgment is a form of thinking in which something is affirmed or denied about the surrounding world, objects, phenomena, as well as relationships and connections between them. Judgments in logic consist of a subject (what the judgment is about), a predicate (what is said about the subject), a copula (what connects the subject and the predicate) and a quantifier (the scope of the subject). Judgments can be of various types: simple and complex, categorical, general, particular, individual. The forms of connectives between the subject and the predicate also differ: equivalence, intersection, subordination and compatibility. In addition, within the framework of composite (complex) judgments there can be their own connectives, which define six more types of complex judgments. The ability to think logically presupposes the ability to correctly construct various types of judgments, understand their structural elements, features, relationships between judgments, and also check whether a judgment is true or false.

Before moving on to the last third form of thinking (inference), it is important to understand what logical laws exist, or, in other words, objectively existing rules for constructing logical thinking. Their purpose, on the one hand, is to help build inferences and argumentation, and on the other hand, to prevent errors and violations of logic associated with reasoning. This lesson will examine the following laws of formal logic: the law of identity, the law of excluded middle, the law of contradiction, the law of sufficient reason, as well as De Morgan's laws, the laws of deductive inference, Clavius' law and the laws of division. By studying examples and completing special exercises, you will learn how to purposefully use each of these laws.

Inference is the third form of thinking in which from one, two or more propositions, called premises, a new proposition, called a conclusion or conclusion, follows. Inferences are divided into three types: deductive, inductive and analogical inferences. In deductive inference (deduction), a conclusion is drawn from a general rule for a particular case. Induction is inference in which a general rule is derived from several particular cases. In inferences by analogy, based on the similarity of objects in some characteristics, a conclusion is drawn about their similarity in other characteristics. In this lesson you will become familiar with all types and subtypes of inferences and learn how to build various cause-and-effect relationships.

This lesson will focus on multi-premise inferences. Just as in the case of single-premise conclusions, all the necessary information in a hidden form will already be present in the premises. However, since there will now be many premises, the methods for extracting them become more complex, and therefore the information obtained in conclusion will not seem trivial. In addition, it should be noted that there are many different types of multi-premise inferences. We will focus only on syllogisms. They differ in that both in the premises and in the conclusion they have categorical attributive statements and, based on the presence or absence of some properties in objects, they allow one to draw a conclusion about the presence or absence of other properties in them.

In previous lessons we talked about various logical operations that form an important part of any reasoning. Among them were operations on concepts, definitions, judgments and inferences. This means that at this point it should be clear what components the reasoning consists of. However, we have not yet touched upon the questions of how reasoning as a whole can be organized and what types of reasoning there are in principle. This will be the topic of the last lesson. Let's start with the fact that reasoning is divided into deductive and plausible. All types of inferences discussed in previous lessons: inferences using a logical square, appeals, syllogisms, enthymemes, sorites, are precisely deductive reasoning. Their distinctive feature is that the premises and conclusions in them are connected by a relation of strict logical consequence, while in the case of plausible reasoning there is no such connection. First, let's talk more about deductive reasoning.

How to take classes?

The lessons themselves with all the exercises can be completed in 1-3 weeks, having mastered the theoretical material and practiced a little. But to develop logical thinking, it is important to study systematically, read a lot and constantly train.

For maximum effect, we recommend that you first simply read all the material, spending 1-2 evenings on it. Then take 1 lesson daily, doing the necessary exercises and following the suggested recommendations. After you have mastered all the lessons, engage in effective repetition in order to remember the material for a long time. Next, try to apply logical thinking techniques more often in life, when writing articles, letters, when communicating, in disputes, in business, and even in your leisure time. Reinforce your knowledge by reading books and textbooks, as well as using additional material, which will be discussed below.

Additional material

In addition to the lessons in this section, we tried to select a lot of useful material on the topic under consideration:

• Logic problems;
• Tests for logical thinking;
• Logic games;
• The smartest people in Russia and the world;
• Video lessons and master classes.

As well as books and textbooks, articles, quotes, auxiliary trainings.

Books and textbooks on logic

On this page we have selected useful books and textbooks that will help you deepen your knowledge of logic and logical thinking:

• "Applied Logic". Nikolai Nikolaevich Nepeyvoda;
• "Textbook of Logic". Georgy Ivanovich Chelpanov;
• "Logic: lecture notes." Dmitry Shadrin;
• "Logics. Training course" (educational and methodological complex). Dmitry Alekseevich Gusev;
• “Logic for Lawyers” (collection of problems). HELL. Getmanova;