Ministry of Education and Science of the Russian Federation. Moscow State Academy of Public Utilities and Construction
Book: LOGIC FOR LAWYERS: LECTURES. / Law College LNU. Franco
2. Logic as a science: its subject, method, as well as the practical significance of its knowledge.
When determining the subject of the science of logic in the logico-philosophical literature, they take into account three aspects: ontological (philosophical doctrine of being), epistemological (cognitive) and formal-logical . AT ontological aspect, the objective basis of the science of logic is determined - the objective existence of objects, phenomena, processes (empirical objects), between which there are various relationships (causal, spatial, temporal, genetic, etc.), that is, what is called the "logic of things". AT epistemological (late rampant) aspect the process of displaying the "logic of things", "logic of events" in the "logic of concepts" and the formation of a system of concepts (categories) that cover the essence of objectively existing things, phenomena and processes are determined. AT formal-logical aspect the necessary interconnections between the logical forms of thinking (concepts, judgments, inferences) are determined, which are determined not by the content of thinking, but only by its structure. All these aspects appear in unity. Given this unity, we can give the following definition of the subject matter of the science of logic:
Logic is a science that studies the laws and forms of human mental activity, the principles and means of building correct judgments and reasoning about objects and phenomena of the objective world, methods of formalizing knowledge as a result of the cognitive process.
Features of logic as a science:
- studies the laws and forms of mental activity of people based on the analysis of theirlanguage utterances, that is, through the implementation (materialization) of the results of mental activity in the language; creates its own specific language (logical language) to analyze the structure of thinking and formalize knowledge.
- the study of logic requires concentration and a systematic approach. All sections of the textbook are interconnected, it is impossible to understand the next topic without mastering the previous one. Learning logic takes a lot of time and effort. As one wise man said: "In the waters of logic, one should not sail with raised sails."
- assimilation theoreticallyThis material from logic does not yet mean that a person will be able to apply it in practice. It is possible to find a way out of this situation by combining theory with the solution of practical problems. In this regard, after studying a particular topic, it is recommended to complete the appropriate practical tasks, as well as consciously apply the acquired logical skills as often as possible in Everyday life, when writing control and term papers, mastering the material of legal disciplines, in discussions, disputes, etc. Only under these conditions can a person learn to think logically correctly, avoiding elementary logical errors in his reasoning and recognizing them in the reasoning of other people.
As a result of successful acquisition theoretical material and working it out in practice, the student will be able to:
♦ identify the main concepts in the text, find out their structure, establish the relationship between them;
♦ logically correctly divide, classify, define concepts;
♦ find errors in sections, classifications, definitions, criticize them and avoid them in your reasoning;
♦ identify the logical structure of statements and interpret them on the basis of this;
♦ reason in accordance with the laws of logic; find pardons in the texts and reasonings of other people related to their violation;
♦ analyze question-answer situations, logically correctly ask questions and give answers to them;
♦ show the reasoning, assumptions and consequences contained in the text;
♦ draw rational conclusions from the available information in accordance with the rules and laws of logic;
♦ logically competently build your reasoning and find errors in the reasoning of opponents;
♦ construct correct argumentation;
♦ convincingly criticize the opponent's arguments;
♦ avoid common mistakes in argumentation and criticism;
♦ to recognize methods of manipulating the interlocutor and resist them.
Mastering the skills of logical thinking is of particular importance for lawyers, whose specific work is the constant use of logical techniques and methods: definitions and classifications, divisions, arguments, rebuttals, etc.
Knowledge of logic greatly helps a lawyer:
♦ analyze legal terminology in codes and other regulations; find out whether a certain norm follows from other norms, its inclusion in a legal document will not be superfluous, whether a new normative act is an addition or a denial of the old one, etc.;
♦ apply logical methods in the process of criminal-legal qualification of a crime;
♦ build forensic and investigative versions using the methods of logic;
♦ draw up clear plans for investigating crimes;
♦ apply logical methods in the process of predicting crime and evaluating the activities of law enforcement agencies;
♦ not to make logical mistakes when drawing up official documents: protocols of interrogation and inspection of the scene, decisions and resolutions, reports, contracts, etc.;
♦ conduct disputes at a high level in court: defend
own opinion and criticize the opinion of the enemy; quickly find logical errors during the trial;
♦ apply logic methods to research scientific problems in jurisprudence.
| 1. | LOGIC FOR LAWYERS: LECTURES. / Law College LNU. Franco |
| 2. | 2. Logic as a science: its subject, method, as well as the practical significance of its knowledge. |
| 3. | 3. Historical stages in the development of logical knowledge: the logic of ancient India, the logic of ancient Greece |
| 4. | 4. Features of general or traditional (Aristotelian) logic. |
| 5. | 5. Features of symbolic or mathematical logic. |
| 6. | 6. Theoretical and practical logic. |
| 7. | Topic 2: THINKING AND SPEECH 1. Thinking (reasoning): definition and features. |
| 8. | 2. Activity and thinking |
| 9. | 3. Structure of thinking |
| 10. | 4. Correct and incorrect reasoning. The concept of a logical error |
| 11. | 5. Logical form of reasoning |
| 12. | 6. Types and types of thinking. |
| 13. | 7. Features of the thinking of a lawyer |
| 14. | 8. Significance of logic for lawyers |
| 15. | Topic 3: Semiotics as a science of signs. Language as a sign system. 1. Semiotics as the science of signs |
| 16. | 2. The concept of a sign. Types of signs |
| 17. | 3. Language as a sign system. language signs. |
| 18. | 4. The structure of the sign process. Sign value structure. Common Logic Errors |
| 19. | 5. Dimensions and levels of the sign process |
| 20. | 6. The language of law |
| 21. | Section III. METHODOLOGICAL FUNCTION OF FORMAL LOGIC 1. Method and methodology. |
| 22. | 2. Logical methods of research (cognition) |
| 23. | 3. Formalization method |
| 24. | BASIC FORMS AND LAWS OF ABSTRACT-LOGICAL THINKING 1. General characteristics of the concept as a form of thinking. Concept structure |
| 25. | 2. Types of concepts. Logical characteristics of concepts |
| 26. | 3. Types of relationships between concepts |
| 27. | 4. Operations with concepts 4.1. Limitation and generalization of concepts |
| 28. | 4.2. Concept division operation |
| 29. | 4.3. Addition, multiplication and subtraction of concepts (more precisely, their volumes) |
| 30. | 4.4 Concept definition operation |
| 31. | BASIC FORMS AND LAWS OF ABSTRACT-LOGICAL THINKING II. Statements. 1. General characteristics of the statement |
| 32. | 2. Truth and falsity of the statement. |
| 33. | 3. Simple statements, their structure and types |
| 34. |
Theoretical question:
TOPIC: “The subject of logic. The specifics of logic and its place among others
sciences that study thinking.
PLAN
Plan ............................... ................... ........... .............................. ........ one
Introduction ............................... ................... .......................................... . 2
1. The subject of logic as a science. ………………………....................... 3
2. The specifics of logic as a science …………………....…………...... 9
3. The place of logic among other sciences that study thinking...... 11
Conclusion.................... ............................. . .............................. ........ 13
List of references .............................................................. fourteen
Exercises ………………………………………………………....15
INTRODUCTION
In the system of humanities logic belongs special place its importance cannot be overestimated. Logic helps to prove true narrowings and refute false ones, it teaches us to think clearly, concisely, correctly, it is the observance of its rules that protects us from erroneous conclusions. In fact, logic was created by Aristotle as a science that makes it possible to distinguish correct definitions and conclusions from incorrect ones and thereby reveal errors in reasoning and public speeches of speakers. At present, interest in logic is caused by many circumstances, and first of all by a significant expansion of the scope of logical knowledge, the specific field of application of which is law.
High requirements for lawmaking, law enforcement practice and legal theory also apply to the professional thinking of a lawyer and are relevant in a modern legal society. At the same time, being logically prepared, the lawyer will be able to accurately and reasonably build his arguments, identify inconsistencies in the testimony of victims, witnesses, suspects, in written sources. Logic will help him convincingly refute the erroneous arguments of opponents, correctly draw up a work plan, official documents, build investigative versions, etc.
Obviously, the study of logic by a lawyer cannot replace special legal knowledge. However, it helps to ensure that every future lawyer becomes a good specialist in his field. No wonder the famous Russian lawyer A.F. Koni believed that an educated lawyer should be a person in whom general education goes ahead of special education. And in the system of general education, one of the leading places belongs to formal-logical training. That is why, according to the outstanding domestic teacher K.D. Ushinsky, logic should be on the threshold of all sciences. At the same time, knowledge of the rules and laws of logic is not the ultimate goal of its study. The ultimate goal of studying logic is the ability to apply its rules and laws in the process of thinking.
1. The subject of logic as a science.
Term "LOGICS" comes from the ancient Greek word??????
- "the science of reasoning", "the art of reasoning" - from?????
- which means "thought", "reason", "word", "speech", "reasoning", "regularity", and is currently used in three main meanings. Firstly, to designate any objective regularity in the interconnection of phenomena, for example, "the logic of facts", "the logic of things", "the logic of history" and so on. Secondly, to denote patterns in the development of thought, for example, "the logic of reasoning", "the logic of thinking" and so on. Thirdly, the science of the laws of correct thinking is called logic. Consider logic in its final meaning.
Thinking is studied by many sciences: psychology, cybernetics, physiology and others. A feature of logic is that its subject is the forms and methods of correct thinking.. So, Logic is the science of the ways and forms of correct thinking.
The main type of thinking is conceptual (or abstract-logical). It is this that is investigated by logic, that is, the object of logic is abstract thinking.
Abstract thinking- this is the process of rational * reflection of the objective world in concepts, judgments, conclusions, hypotheses, theories, which allows one to penetrate into the essence, into the regular connections of reality, to creatively transform it first in theory, and then in practice.
As you know, all objects, phenomena and processes have both content and form. Our knowledge of form is quite diverse. The logical form is also understood in many ways. Our thoughts are made up of some meaningful parts. The way they are connected represents the form of thought.
So, various objects are reflected in abstract thinking in the same way - as a certain connection of their essential features, that is, in the form of a concept. The form of judgments reflects the relationship between objects and their properties. Changes in the properties of objects and relations between them are reflected in the form of inferences.
* Rational (from lat. ratio - mind) - related to the mind, reasonableness of the mind, accessible to reasonable understanding.
Consequently, each of the main forms of abstract thinking has something in common that does not depend on the specific content of thoughts, namely: the way the elements of thought are connected - signs in a concept, concepts in a judgment, and judgments in a conclusion. The content of thoughts determined by these connections does not exist by itself, but in certain logical forms: concepts, judgments and conclusions, each of which has its own specific structure.
Take, for example, two statements: "Some lawyers are teachers" and "Some socially dangerous acts are a crime against the personal property of citizens." Let us replace all their meaningful components with symbols. Let's say that what we think about - with the Latin letter S, and what we think about S - with the Latin letter P. As a result, we get the same elements of thought in both cases: "Some S are P." This is the logical form of the given judgments. It is obtained as a result of abstraction from specific content.
In this way, logical form(or a form of abstract 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 an inseparable unity. There is no pure, formless content, no pure, meaningless logical forms. For example, the above logical form of the propositions "Some S are P" does have some content. From it we learn that every object of thought denoted by the letter S (subject) has a sign denoted by the letter P (predicate). Moreover, the word "some" shows that the attribute P belongs to only a part of the elements that make up the subject of thought. This is the "formal content".
However, for the purposes of a special analysis, we can digress from the specific content of thought, making its form the subject of study. The study of logical forms, regardless of their specific content, is the most important task of the science of logic. Hence its name - formal.
At the same time, it should be borne in mind that formal logic, while investigating the forms of thinking, does not ignore its content. Forms, as has already been canceled, are filled with specific content, are associated with a completely defined, specific, subject area. Outside of this concrete content, the form cannot exist, and in itself does not determine anything from a practical point of view. The form is always meaningful, and the content is always formalized. With these aspects of thinking, the distinction between its truth and correctness is connected. Truth refers to the content of thoughts, and correctness to their form.
Considering the truth of thinking, formal (two-valued) logic proceeds from the fact that truth is understood as the content of thought that corresponds to reality itself. The concept of "truth" in the legal sphere is closely related to the concept of "truth" ("I undertake to tell the truth and only the truth!"). Truthful is not only true, but also correct, honest, fair. If the thought in its content does not correspond to reality, then it is false. From here truth of thought- this is its fundamental property, manifested in the ability to reproduce reality as it is, to correspond to it in its content. BUT falsity- the property of thinking to distort this content, to pervert it.
Another important characteristic of thinking is its correctness. Right thinking- this is its fundamental property, which also manifests itself in relation to reality. It means the ability of thinking to reproduce in the structure of thought the objective structure of being, to correspond to the actual relations of objects and phenomena. And vice versa, the incorrectness of thinking means its ability to distort the structural connections and relationships of being.
Formal logic is abstracted from the concrete content of thoughts,
not content in general. Therefore, it takes into account the truth or falsity of the propositions under study. However, it transfers the center of gravity to the correctness of thinking. Moreover, the logical structures themselves are considered regardless of their logical content. Since the task of logic is to analyze exactly correct thinking, it is also called logical thinking after the name of this science. Correct (logical) thinking has the following essential features or PROPERTIES: certainty, consistency, consistency and validity.
Certainty- this is the property of correct thinking to reproduce in the structure of thought the real signs and relationships of the objects and phenomena themselves, their relative stability. It finds its expression in the accuracy and clarity of thought, the absence of inconsistency and confusion in the elements of thought and the thoughts themselves.
Consistency - the property of correct thinking to avoid contradictions in the structure of thought that do not exist in the reflected reality. It manifests itself in the inadmissibility of logical contradictions in rigorous reasoning.
Subsequence- the property of correct thinking to reproduce by the structure of thought those structural connections and relationships that are inherent in reality itself, the ability to follow the “logic of things and events”. It is revealed in the consistency of thought to itself.
Validity there is a property of correct thinking to reflect objective causal relationships and relationships of objects and phenomena of the surrounding world. It manifests itself in establishing the truth or falsity of a thought on the basis of other thoughts, the truth of which has been established earlier.
These essential features of correct thinking are not arbitrary. They are the result of human interaction with the outside world. They can neither be identified with the fundamental properties of reality itself, nor separated from them. The correctness of thinking, reflecting, first of all, the objective laws of the world, arises and exists spontaneously, long before the emergence of any rules whatsoever. The logical rules themselves are only milestones on the way to comprehending the features of correct thinking, the laws operating in them, which are immeasurably richer than any, even the most complete, set of such rules. But the rules are developed on the basis of these laws precisely in order to regulate subsequent mental activity, to ensure its correctness already consciously.
Thus, the logical correctness of reasoning is due to the laws of abstract thinking. Violation of the requirements arising from them leads to logical errors. Law of thought- this is a necessary, essential, stable connection of thoughts in the process of reasoning. These laws are the same for all people, regardless of their social and national affiliation. Logical laws act independently of the will of people, they are not created at their will. They are a reflection of the connections of things in the objective world. At the same time, a person is not simply included in the scope of a certain logical law, not only passively submits to its regulatory influence, but also develops a conscious attitude to objectively occurring thought processes. The knowledge of the laws of logic, the definition of their objective basis, allows us to put forward and formulate its principles. The principles of formal logic, like the principles of any science, represent the unity of the objective and the subjective. On the one hand, they express the objective content of the laws of logic, on the other hand, they act as the rules of human mental activity. It is through the conscious formulation of principles that the laws of logic become regulators of people's mental activity.
Thus, formal logic, in order to be a means of discovering truth, must, on the basis of studying the formal structures of abstract thinking, preserve and take into account the logical correctness of reasoning, due to logical laws.
What aspects of abstract thinking are studied by formal logic? Firstly, it considers abstract thinking as a tool for understanding the world, as a means of obtaining formally true knowledge.
Secondly, it is interested in the practical effectiveness and correctness of indirect (inferential) knowledge obtained from previously established and verified truths without resorting to experience, but only as a result of taking into account formal logical laws and applying the corresponding rules of abstract thinking.
Thirdly, abstract thinking is considered as a formal process that has its own special structure, which differs from the structure of the objectively true content of thinking.
That is why formal logic allows one to abstract from the content of an object and focus only on the forms in which one or another thought process takes place. These aspects of the interdependence of Logic and thinking determine the features of formal logic as a science.
So, formal logic- this is the science of generally valid forms and means of thought necessary for the rational knowledge of being and its specific types. Commonly valid forms of thought include concepts, judgments, and conclusions. The generally significant means of thought are the rules (principles), logical operations, techniques and procedures, the formal-logical laws underlying them, that is, everything that serves the purpose of implementing correct abstract thinking.
Therefore, the subject of formal logic is:
1) forms of the thought process - concept, judgment, conclusion, hypothesis, proof, etc.;
2) the laws that abstract thinking obeys in the process of cognizing the objective world and thinking itself;
3) methods for obtaining new output knowledge - similarities, differences, concomitant changes, residues, etc.;
4) ways to prove the truth or falsity of the knowledge gained - direct or indirect confirmation, refutation, etc.
Thus, logic in the broadest sense of its subject explores the structure of abstract thinking, reveals the patterns underlying it. However, abstract thinking, generalized, indirectly and actively reflecting reality, is inextricably linked with language. Language expressions are that reality, the structure and method of use of which gives us knowledge not only about the content of thoughts, but also about their form, about the laws of thinking. Therefore, in the study of linguistic expressions and the relationships between them, logic sees one of its main tasks.
2. Specificity of logic as a science
Logic as a science includes such sections as formal logic, dialectical, symbolic, modal and others. The purpose of this work is formal logic.
The principles and rules of logic are universal in nature, since in any science conclusions are constantly drawn, concepts are defined and refined, statements are formulated, facts are generalized, hypotheses are tested, etc. From this point of view, every science can be considered as applied logic. But especially close links exist between logic and those sciences that are engaged in the study of human mental activity, both on an individual and social level.
A clear delimitation of the areas of study of the sciences of spiritual activity is directly related to the definition of the subject and methods of studying logic.
The view of logic as a technology of thinking also has a number of attractive features, if only because in practice we most of all need to skillfully use the rules of reasoning, recommendations on how to effectively find arguments (premisses for conclusions), build and test hypotheses, - in a word, all that is characterized as the art of thinking or guessing.
The nature of the laws of logic as a science is that they reflect the main, constantly occurring connections and relationships that exist in the real world. That is why logic can be applied to study them. But the real world, its specific patterns serve as the subject of study of specific natural, social and technical sciences. Through the analysis of concepts, judgments and inferences used in these sciences, logic plays its role - a theoretical tool that serves to control the correctness and validity of reasoning and thereby contribute to the search and proof of truth.
The applied role of logic in specific sciences is not limited to the direct analysis of reasoning. Its methods are widely used in the methodology of scientific knowledge to analyze such forms of scientific thinking as hypothesis, law, theory, as well as to reveal the logical structure of explanation and prediction, as the most important functions of any science. This direction of applied research in recent decades has laid the foundation for the logic of science in which the concepts, laws and methods of logic are successfully used to study not only purely logical, but also methodological problems that arise in scientific knowledge.
In modern conditions of the development of social processes in Russia, logic, as a science, does not lose its relevance. This is due to two main factors. One of them - features of the current stage of development of society itself. This stage is characterized by an ever greater increase in the role of science in the development of all aspects of social life, its penetration into all pores of the social organism. Accordingly, the significance of logic, which explores the means and patterns of scientific knowledge, is also enhanced. And in the conditions of modernization of the Russian economy, which requires understanding of new, complex, diverse economic and social processes occurring in the life of society, the role of science, and hence logic, increases many times over.
Another circumstance - new, high-quality breakthrough of scientific and technological progress. In the 21st century, science and technology open up horizons of knowledge unknown to society before the village, and fundamental research allows one to penetrate the secrets of the universe. At the same time, the importance of abstract thinking, and in this connection the growing importance of logic, which studies its structure, forms and laws, cannot be overestimated. In modern conditions of the deployment of a new stage of the scientific and technological revolution, associated with deep structural and informational changes in production and management, the introduction of the achievements of cybernetics and nanoindustry, the need for logic, especially symbolic, becomes even more tangible and necessary.
3. The place of logic among other sciences that study thinking.
Logic is a complex, multifaceted phenomenon of the spiritual life of mankind. Currently, there is a great variety of different industries scientific knowledge. Depending on the object of study, they are divided into natural sciences - natural sciences and social sciences - social sciences. In comparison with them, the originality of logic lies in the fact that its object is thinking.
What is the place of logic among other sciences that study thinking?
Philosophy is the study of thought in general. It solves a fundamental philosophical question related to the relationship of a person and his thinking to the world around him.
Psychology studies thinking as one of the mental processes along with emotions, will, etc. It reveals the interaction of thinking with them in the course of practical activity and scientific knowledge, analyzes the motives of human mental activity, reveals the peculiarities of thinking in children, adults, mentally normal people and persons with disabilities.
Physiology reveals material, physiological processes, explores the patterns of these processes, their physicochemical and biological mechanisms.
Cybernetics reveals the general patterns of control and communication in a living organism, a technical device and in a person's thinking, associated primarily with his managerial activity.
Linguistics shows the inseparable connection between thinking and language, their unity and difference, their interaction with each other. It reveals ways of expressing thoughts with the help of linguistic means.
The originality of logic as a science of thinking lies precisely in the fact that it considers this object common to a number of sciences from the point of view of its functions and structure, that is, the role and significance in cognition and practical activity, and at the same time from the point of view of its constituent elements, as well as the connections and relationships between them. This is its own, specific subject of logic. Therefore, it is defined as the science of the forms and laws of correct thinking, leading to the truth.
There is an opinion that the ability to reason logically is inherent in people by nature. It is erroneous.
But if a logical culture is not given to a person by nature, then how is it formed?
The logical culture of thinking is mastered in the course of communication, study at school and university, in the process of reading literature. Meeting repeatedly with one or another way of reasoning, we gradually assimilate them and begin to understand which of them are correct and which are not. The logical culture of a lawyer increases in the course of his professional activity.
The specified way of formation of logical culture can be called spontaneous. It is not the best, since people who have not studied logic, as a rule, do not own certain logical techniques, and, in addition, they have a different logical culture, which does not contribute to mutual understanding.
The value of logic for lawyers.
The specifics of the work of a lawyer lies in the constant use of special logical techniques and methods: definitions and classifications, arguments and rebuttals, etc. The degree of mastery of these techniques, methods and other logical means is an indicator of the level of the logical culture of a lawyer.
Knowledge of logic is an integral part of legal education. It allows you to correctly build forensic and investigative versions, draw up clear plans for investigating crimes, avoid mistakes in the preparation of official documents, protocols, indictments, decisions and decrees.
Famous lawyers have always used the knowledge of logic. In court, they usually did not limit themselves to simple disagreement, for example, with the arguments of the prosecution, if they saw in them a logical error. They explained what mistake was made, said that this mistake is specially considered in logic and has a special name. This argument affected everyone present, even if those present had never studied logic.
Knowledge of the rules and laws of logic is not the ultimate goal of its study. The ultimate goal of studying logic is the ability to apply its rules and laws in the process of thinking.
Truth and logic are interconnected, so the value of logic cannot be overestimated. Logic helps to prove true narrowings and refute false ones; it teaches to think clearly, concisely, and correctly. Logic is needed by all people, workers of various professions.
Conclusion
Human thinking is subject to logical laws and proceeds in logical forms, regardless of the science of logic. Many people think logically without knowing its rules. Of course, one can think correctly without studying logic, but one cannot underestimate the practical significance of this science.
The task of logic is to teach a person to consciously apply the laws and forms of thinking and on the basis of this it is more logical to think, to correctly recognize the world around him. Knowledge of logic increases the culture of thinking, develops the ability to think "competently", develops a critical attitude towards one's own and other people's thoughts.
Logic is a necessary tool that frees from personal, unnecessary memorization, helping to find in the mass of information that valuable thing that a person needs. It is needed "by any specialist, whether he is a mathematician, a physician, a biologist." (Anokhin N.K.).
To think logically means to think accurately and consistently, not to allow contradictions in one's reasoning, to be able to reveal logical errors. These qualities of thinking are of great importance in any field of scientific and practical activity, including the work of a lawyer.
Knowledge of logic helps a lawyer prepare a logically coherent, well-reasoned speech, reveal contradictions in testimony, and so on. All this is important in the work of a lawyer, aimed at strengthening the rule of law and order.
List of used literature:
1. Geitmanova A.D. Logic textbook. Moscow 1995
2. Demidov I.V. Logic - tutorial Moscow 2000
3. Ruzavin G.I. Logic and reasoning. Moscow 1997
4. A short dictionary of logic. Under the editorship of Gorsky. Moscow Enlightenment 1991
5. Kirillov V.I., Starchenko A.A. Logics. Edition 5th 2004
Exercises:
1. Set the content and scope of the following concepts: natural phenomenon, natural disaster, earthquake.
etc.................
Moscow State Academy of Public Utilities and Construction
(name of the department)
________________________________________________________________
(surname, name, patronymic of the student)
Faculty ______________ course ____________ group _____________
TEST
By discipline _________________________________________________
On the topic __________________________________________________
(topic name) ________________________________________________________________
Mark of offset _________________________ __________
(pass/fail) (date)
Supervisor __________________________________ __________________
(full name, position, academic degree, academic title) (signature)
Moscow 20__
TEXTS OF LECTURES
TO THE COURSE OF THE EDUCATIONAL DISCIPLINE "LOGIC"
Topic 1. SUBJECT AND SIGNIFICANCE OF LOGIC
1.1. The concept of "logic", its main meanings. The place of logic in the system of the sciences of thinking.
Term "logics" comes from the Greek word logos, which means "thought", "word", "reason", "regularity", and is used both to refer to the set of rules that the process of thinking obeys, and to refer to the science of the rules of reasoning and those forms in which it is carried out. In addition, this term is used to refer to any patterns ("logic of things", "logic of events").
The study of thinking occupies one of the central places in all philosophical teachings both past and present. Thinking is studied not only by logic, but also by a number of other sciences - philosophy, physiology, cybernetics, linguistics, each highlights its own aspect of study:
Philosophy- studies the relationship between matter and thought.
Sociology- analyzes historical development depending on the social structures of society.
Cybernetics- studies thinking as an information process.
Psychology- studies the mechanisms for the implementation of mental acts, including brain ones, and understands thinking as a cognitive activity.
The role of thinking in cognition.
A person from the first days of his life is included in the process of cognition of the world around him. He recognizes individual signs of objects and phenomena that are reflected in sensations. ; holistic objects and phenomena in their immediate givenness to a person are presented in perception ; visible and invisible to the human eye connections and relationships between objects and phenomena allows you to open thinking . In a broad sense, a person's thinking is understood as his active cognitive activity with an internal process of planning and regulating external activities. To understand how a person thinks means to understand how he sees (represents, reflects) the world around him, himself in this world and his place in it, and also how he uses knowledge about the world and about himself to control his own behavior.
Cognition is the construction of the semantic (ideal) content of the world in the minds of people. The world and its properties are revealed in the process of cognition. Practice is one of the elements of knowledge. In practical activities, people encounter various properties of objects and phenomena. Knowledge has two main stages: sensual and rational.
Thought activity receives all its material from only one source - from sensory cognition. Sense cognition has three main forms: sensation, perception and performance. Through sensations and perceptions, thinking is directly connected with the external world and is its reflection. The correctness (adequacy) of this reflection is continuously tested in the process of practical transformation of nature and society.
Feeling- a subjective image of the objective world, the transformation of the energy of external irritation into a fact of consciousness.
Any empirical knowledge begins with living contemplation, sensory perceptions. Forms of sensory perception are reflections of individual properties of objects or phenomena that directly affect the senses. Each item has not one, but many properties. Feelings reflect various properties of objects.
Perception- this is a reflection in the human mind of integral complexes of properties of objects and phenomena of the objective world with their direct impact at a given moment on the senses.
Performance- this is a sensual image of an object that is not currently perceived, but which was previously perceived in one form or another. The representation can be reproducing (for example, everyone now has an image of their home, their workplace, images of some acquaintances and relatives whom we do not see now), creative, including fantastic. Through sensory perception, a person discovers the phenomenon of an object, but not its essence. The laws of the world, the essence of objects and phenomena, the general in them a person learns through abstract thinking, which represents the world and its processes deeper and more fully than sensory perception. The transition from sensory perception to abstract thinking is a qualitatively different level in the process of cognition. This is the transition from the primary presentation of facts to the knowledge of laws.
The main forms of the abstract, i.e. abstract from the directly given reality of thinking, are concepts, judgments and conclusions.
concept- a form of thinking that reflects the essential properties, connections and relationships of objects and phenomena, expressed by a word or a group of words. Concepts can be general and singular, concrete and abstract.
Judgment - a form of thinking that reflects the relationship between objects and phenomena; assertion or denial of something. Judgments can be true or false.
inference- a form of thinking in which a certain conclusion is made on the basis of several judgments. It is a series of logically connected statements from which new knowledge is derived.
Example: All those present at the lecture are students. Olya is present at the lecture (2 judgments). Olya is a student (inference).
Distinguish inferences inductive, deductive and Similarly.
In the process of logical knowledge, a person strives to reach the truth. Logical truth, or truth, is the correspondence of an inference to the rules of thought that are established for it. This will mean that the premises and the conclusion following from them are combined logically "correctly", i.e. correspond to the criterion of truth established for a given logical system. The task of any logical system is to show what are the rules for combining individual meanings and what conclusions this combination leads to. These conclusions will be what is called logical truth.
An essential feature of abstract thinking is its inseparable connection with language, since the laws of occurrence, combination, and expression of linguistic meanings are identical to the functioning of logical meanings. This means that any phrase, sentence or combination of sentences has a certain logical meaning.
1.3. The main stages in the development of logic
The emergence of logic as a theory was preceded by the practice of thinking going back thousands of years.
History shows that individual logical problems arise before the mind's eye of man already over 2.5 thousand years ago - first in ancient india and ancient China. Then they get a more complete development in Ancient Greece and Rome. Only gradually do they develop into a more or less coherent system, taking shape as an independent science.
Reasons for the emergence of logic. First, the origin and initial development of the sciences in Ancient Greece (VI century BC), primarily mathematics. Born in the struggle with mythology and religion, science was based on theoretical thinking, involving inferences and proofs. Hence the need to study the nature of thinking itself as a form of cognition. Logic arose, first of all, as an attempt to identify and explain the requirements that scientific thinking must satisfy in order for its results to correspond to reality. Another reason is the development oratory, including the judiciary, which flourished in the conditions of ancient Greek polar democracy.
Formal logic has gone through two main stages in its development.
First stage related to work ancient Greek philosopher and the scholar Aristotle (384-322 BC), who was the first to give a systematic exposition of logic. Aristotle's logic and all pre-mathematical logic are usually called "traditional" formal logic. Traditional formal logic included and includes such sections as concept, judgment, inference (including inductive), laws of logic, proof and refutation, hypothesis. Aristotle gave a classification of the most general concepts - a classification of judgments, fundamental laws of thinking - the law of identity, the law of the excluded middle. Logic itself was further developed both in Greece and elsewhere.
A significant contribution to the development of logic was made by medieval scholastics. The Latin terminology introduced by them is still preserved.
During the Renaissance, logic was in crisis. It was regarded as the logic of "artificial thinking", which was opposed to natural thinking, based on intuition and imagination.
A new stage in the development of logic begins in the 17th century. This is due to the creation within its framework, along with deductive logic, of inductive logic. The need for obtaining such knowledge was most fully realized and expressed in his writings by the outstanding English philosopher and naturalist Francis Bacon(1561-1626). He became the founder of inductive logic, writing in contrast to the old "Organon" by Aristotle "New Organon ...".
Inductive logic was later systematized and developed by the English philosopher and scientist John Stuart Mill(1806-1873) in his two-volume work "The System of Syllogistic and Inductive Logic".
The need for scientific knowledge not only in the inductive, but also in the deductive method in the 17th century. most fully embodied by the French philosopher and scientist Rene Descartes(1596-1650). In his main work "Reasoning about the method ...", based on data, primarily mathematics, he emphasizes the importance of rational deduction.
Followers of Descartes from the monastery at Port-Royal A. Arno and P. Nicole created the work "Logic, or the Art of Thinking". It became known as "The Logic of Port-Royal" and was used for a long time as a textbook on this science.
Second phase - this appearance mathematical (or symbolic) logic.
Growing successes in the development of mathematics and the penetration of mathematical methods into other sciences in the second half of the 17th century. strongly raised two fundamental problems. On the one hand, this is the application of logic to develop the theoretical foundations of mathematics, and on the other hand, the mathematization of logic itself as a science.
largest German philosopher and mathematician G. Leibniz(1646-1716) is rightfully considered the founder of mathematical (symbolic) logic, since it was he who used the formalization method as a research method. However, the most favorable conditions for the powerful development of mathematical (symbolic) logic were obtained in the works D. Boole, E. Schroeder, P. S. Poretsky, G. Frege and other logicians. By this time, the mathematization of sciences had made significant progress, and new fundamental problems of its justification arose in mathematics itself.
Thus opened a new modern stage in the development of logical research. Perhaps the most important distinguishing feature of this stage is the development and use of new methods for solving traditional logical problems. This is the development and application of the so-called formalized language - the language of symbols, i.e. alphabetic and other signs (hence the most common name for modern logic - "symbolic").
There are two types of logical calculations: propositional calculus and predicate calculus. In the first case, abstraction from the conceptual structure of judgments is allowed, and in the second case, this structure is taken into account and, accordingly, the symbolic language is enriched, supplemented with new signs.
The formation of dialectical logic. At one time, Aristotle posed and tried to solve a number of fundamental problems dialectical logic- the problem of reflecting real contradictions in concepts, the problem of the relationship between the individual and the general, the thing and the concept of it, etc. Elements of dialectical logic gradually accumulated in the works of subsequent thinkers and were especially clearly manifested in the works Bacon, Hobbes, Descartes, Leibniz. However, as an independent logical science, qualitatively different from formal logic in its approach to thinking, dialectical logic began to take shape only in late XVIII - early XIX centuries
The first who tried to introduce dialectics into logic was the German philosopher I.Kant(1724-1804). Kant believed that logic is "a science that sets out in detail and strictly proves only the formal rules of all thinking ...".
But in this undoubted merit of logic, Kant also discovered its main drawback - limited opportunities as a means of real knowledge and verification of its results. Therefore, along with the "general logic", which Kant for the first time in its history also called "formal logic" (and this name has stuck with it up to the present), a special, or "transcendental logic" is needed. He saw the main task of this logic in the studies of such, in his opinion, really basic forms of thinking as categories: "We cannot think of a single object except with the help of categories ...". They serve as a condition for any experience, therefore they are a priori, pre-experimental in nature. These are the categories of space and time, quantity and quality, cause and effect, necessity and chance, and others. dialectical categories, the application of which allegedly does not comply with the requirements of the laws of identity and contradiction.
A grandiose attempt to develop an integral system of a new, dialectical logic was made by another German philosopher - G. Hegel(1770-1831). In his seminal work, The Science of Logic, he revealed the fundamental contradiction between the available logical theories and the actual practice of thinking, which by that time had reached considerable heights. The means of resolving this contradiction was the creation by him in a peculiar, religious-mystical form of a system of new logic. It focuses on the dialectic of thinking in all its complexity and inconsistency.
The growing needs of scientific and technological progress determine the further intensive development of modern logic.
Topic 2. Language of logic
The subject of the study of logic are the forms and laws of correct thinking. Thinking is a function of the human brain, which is inextricably linked with language.
2.1. Correlation of language and thinking. The concept of sign systems.
Cognitive thinking, studied by logic, is always expressed in language, therefore logic considers thought in its linguistic expression. The functions of natural language are numerous and multifaceted.
Language- a means of everyday communication between people, a means of communication in scientific and practical activities. The language also has such features: to store information, to be a means of expressing emotions, to be a means of cognition. Language is a sign information system, a product of human spiritual activity. The accumulated information is transmitted using the signs (words) of the language.
Speech it can be oral or written, sound or non-sound (for the deaf and dumb), external speech (for others) or internal, speech expressed using natural or artificial language. With the help of scientific language, which is based on natural language, the provisions of all sciences are formulated.
Artificial languages of science arose on the basis of natural languages . These include the languages of mathematics, symbolic logic, chemistry, physics, as well as algorithmic programming languages for computers, which are widely used in modern computers and systems.
Word and concept. Name. The ability to cognize the external world through ideas that reflect objects in their general and essential features creates a generally valid logical form of thinking - concept. Without a concept, it is impossible to formulate laws and single out the subject area of science. The concept helps to identify certain classes of things and distinguish them from each other. The concept acts as a result of abstraction, that is, the mental selection of the essential properties of things and their generalization through distinctive features.
Language serves to express ideas. Names not only designate certain objects, but also express this or that thought. This thought (more precisely, the form of thought) is called a concept.
concept there is a form of thought expressed by a name. Our everyday and professional conversations, speeches, disputes consist of words and sentences.
Among the words we use, names are the most important, since they make up most of the words.
Name- this is a language expression denoting a single object, a set of objects, a property or a relation.
Names are divided into: 1) simple, complex, descriptive; 2) own;3) general. Every name has a meaning, or meaning. The meaning, or meaning of a name, is the way in which the name denotes the subject, that is, the information about the subject contained in the name. Different expressions denoting the same subject have the same meaning or sense.
In logic, a distinction is made between expressions that are named functions and expressions that are propositional functions. Nominal function- this is an expression that, when variables are replaced by constants, turns into a designation of an object. This is the name of an expression that contains a variable and turns into a true or false statement when the name of an object from a certain subject area is substituted for the variable.
At logical analysis language is considered as a sign system.
Sign is a material object used in the process of cognition or communication as a representative of an object.
It is possible to single out signs of the following three types: 1) signs - indices; 2) signs - samples; 3) signs - symbols.
Index signs associated with the objects they represent, or effects with causes.
Sample signs are those signs that in themselves provide information about the objects they represent (a map of the area, a map-drawing), since they are in a relationship of similarity with the designated objects.
Signs-symbols are not connected causally and are not similar to their representation by objects. Logic examines signs of the latter kind.
To the main symbols that replace the main concepts of logic, the concept of a subject, or an object of thought (logical subject) and a predicate, i.e. a sign of the object of thought, inherent or not inherent in it (logical predicate), include S and P. The concepts "subject" and "predicate" are also used in philosophy, so from the very beginning it is necessary to establish, albeit not so radical, but still existing differences between their philosophical and logical meanings. In philosophy, the “subject” is both an individual person and thinking humanity, society as a whole, i.e. something that opposes the "object" - nature, the world as a whole. In logic, the “subject” is the subject of thought, what our consciousness, our attention, intellect, mind is directed to, what the argument is about, this is the logical subject of judgment. It can be any concept that reflects any real or imaginary, material or ideal "object". The subject of thought, therefore, can be anything.
A "predicate" in philosophy and logic almost coincides in its meaning, it is any sign inherent or not inherent in this or that subject, in logic, of course, the subject of thought.
S is a symbol for designating the subject of judgment (subject of thought, logical subject).
P is the symbol of the judgment predicate (logical predicate), i.e. a concept that reflects an attribute inherent or not inherent in the subject of thought (subject).
M - the middle term of the inference, the general length of the original judgments concept.
“Is” - “is not” (essence - not essence, etc.) - a logical link between the subject and the predicate of the judgment, sometimes expressed by a simple dash between “S” and “P”.
R is the symbol of any relation.
A (a) is a symbol of a universally affirmative judgment (“All students are students”).
E (e) is a symbol of a generally negative judgment (“All students in this group are not athletes”, or, which is the same thing, “Not a single student in this group is an athlete”).
I (i) - a symbol of a private affirmative judgment ("Some students are excellent students").
O (o) - a symbol of a private negative judgment ("Some students are not excellent students").
V is the symbol of the quantifier of generality (universality), in the language it is expressed by the word "everything", "for everyone", etc.
I - the symbol of the existence quantifier, in the language it is expressed by the word "some", "there are such", "many", etc.
/ \ - a symbol, or a sign of a connecting logical union "and" (conjunction).
V is a symbol (sign) of the separating logical union "or" (disjunction).
--> - a symbol of a conditional logical union "if .., then ..." (implication).
<-->- a symbol of the logical union of identity, equivalence: "if and only if", "if and only if" (equivalence).
"Not" - a negative particle, can also be expressed with a bar over the sign, for example: B, C.
A symbol to indicate a need.
A symbol to indicate an opportunity.
Artificial languages of science arose on the basis of natural languages. These include the languages of mathematics, symbolic logic, chemistry, physics, as well as algorithmic programming languages for computers, which are widely used in modern computers and systems.
names are language expressions whose substitution into the formula "S is P" instead of the variables S and P gives a meaningful sentence.
The names are, for example, "starry night", "Volga", "Tambov" and "evening twilight". Substitution of these expressions into the indicated form gives meaningful (although not necessarily true) sentences: "Tambov is the Volga", "Evening twilight is a starry night", "Starry night is the Volga", etc.
Suggestion (statement) is a language expression that is true or false.
Functor- this is a linguistic expression that is neither a name nor a statement and serves to form new names or statements from existing ones.
Topic 3. Basic laws of logic
3.1. The concept of "logical law"
Law of thought- this is an internal, necessary connection between thoughts. The simplest and at the same time necessary connections between thoughts are expressed with the help of the main formally logical laws, the obedience to which determines the certainty, consistency, consistency and validity of thinking. Formal logic considers four basic laws: identity, non-contradiction, excluded middle, sufficient reason. These laws express the most general properties of all correct thinking and have a universal and necessary character. Without observing these laws, correct thinking is generally impossible.The first three of these laws were identified and formulated by Aristotle, and the law of sufficient reason was formulated by G. Leibniz.
The study of these laws is necessary and important for understanding the complex deep processes that naturally occur in thinking, regardless of our awareness of them and will, as well as for using these laws in the practice of mental activity. Violation of laws leads to logical contradictions and the inability to distinguish truth from lies.
3.2. The law of identity and its logical requirements for the thinking process, as well as errors due to their violationLaw of Identity establishes the requirement for the certainty of thinking: using a term in the process of thinking, we must understand by it something definite. Therefore, in reasoning it is necessary to leave concepts and judgments the same in content and meaning. This requirement is preserved if each transformation is nullified by its inverse (zero transformation).
The immutability of thought in the course of reasoning is fixed by the formula A is A or A≡A, or not A is not A. The objective basis of the law is in temporary equilibrium, the rest of any body or process.
Even constant movement, change allows you to recognize and identify objects. This objective property of a thing, an event, to retain identity, one and the same quality, must be reflected by thinking, which must grasp the constancy of the object. The law of identity requires that concepts and judgments be unambiguous, without uncertainties and ambiguities.
This brief review shows that the law of identity is universal in the sense of covering all forms of thought without exception, any thought in general.
The requirements of the law of identity and logical errors due to their violation.
Certain requirements follow from the law of identity, which operates objectively in our thinking.
These are logical norms, attitudes, prescriptions or rules that are formulated by people themselves on the basis of the law and which must be observed in order for thinking to be correct, leading to the truth. They can be reduced to the following two:
1) Each concept, judgment, etc., must be used in the same definite sense and retain it in the process of the whole reasoning.
Related to this requirement is the following.
2) It is impossible to identify different thoughts and it is impossible to take identical thoughts for different ones.
Requiring certainty, unambiguity of thought, the law of identity at the same time is directed against any fuzziness, inaccuracy, vagueness of our concepts, etc.
In cases where the requirements of the law of identity are violated, numerous logical errors occur. They are called differently: amphibolia"(ambiguity, i.e., the use of the same homonym word at the same time in different senses), "mixing of concepts", "confusion in concepts", "substitution of one concept for another" ( equivocation), "thesis substitution", etc.
The meaning of the law of identity. Knowledge of the law of identity and its use in the practice of thinking is of fundamental importance, as it allows you to consciously and clearly separate the correct reasoning from the wrong one, to find logical errors - ambiguity, substitution of concepts, etc. - in the reasoning of other people and avoid their own.
In any speech - written or oral - one should, in accordance with the law of identity, achieve clarity of presentation, and it involves the use of words and expressions in the same sense, understandable to others, and in natural combinations with other words.
It is very important to comply with the requirements of the law of identity in discussions, disputes, etc. In order for the dispute not to be pointless, it is always necessary to accurately determine the subject of the dispute and accurately clarify the key concepts in it. For equivalent concepts, you can and should use synonyms. It should only be remembered that synonymy is relative (words that are synonyms in one respect are not synonyms in another). And under the guise of synonyms, completely different concepts are sometimes used. If the words homonyms are used, then it is required to find out exactly the meaning in which they are taken in this case.
3.3. The law of non-contradiction, its constructive role in logical thinkingLaw of non-contradiction expresses the requirement of consistency of thinking and reflects the qualitative certainty of objects. From the standpoint of this remark, an object cannot have mutually exclusive properties, that is, it is impossible, at the same time, the presence and absence of any property in an object.
The formula of the law says: It is not true that A and not A are both true at the same time.
The law of non-contradiction is directly related to the law of identity. If the law of identity speaks of a certain equality of the object of thought to itself, then the law of non-contradiction indicates that “this” object of thought must necessarily be different from all other objects. Thus, the law of non-contradiction has its own content. It is expressed in the following: one and the same object at the same time and in the same sense cannot be attributed opposite signs. If opposite signs are attributed to the same object, then one of them, in any case, is falsely attributed.
Thus, judgments cannot be true at the same time: this person is a good specialist - this person is a bad specialist.
The objective content of the law is in the reflection by thinking of the special binomeric features of reality itself. These opposite features, or constructs, make it possible to classify phenomena and highlight positive and negative phenomena. Without doing this, it is impossible to make a distinction from which mental activity begins. The logical source of the contradiction is an erroneous starting position; the result of thoughtlessness and ignorance of the matter; undeveloped, undisciplined thinking; ignorance and the desire to deliberately confuse the matter.
At the same time, opposite judgments can be true in the following cases:
1) if we are talking about different features of one object;
2) if we are talking about different objects with the same feature;
3) if we are talking about one subject, but it is considered at different times and in different ways.
Scope of the law of non-contradiction. This law is, first of all, a generalization of the practice of operating with judgments. It reflects the natural relationship between two judgments - affirmative and negative, the relationship of their incompatibility in truth: if one is true, then the other is certainly false.
Judgments are divided into affirmative and negative, and they, in turn, into true and false, this explains the universal nature of the law of non-contradiction. Since complex judgments are formed from simple ones, the law of non-contradiction also applies here if they are in relation to negation.
This law also applies to concepts, namely, to the relations between them. This is a relationship of incompatibility.
So, if the forest is "coniferous", then it cannot be "deciduous" (relation of subordination); if a person is "generous", then he cannot be at the same time "ungenerous" (relationship of contradiction) or "stingy" (relationship of opposites).
The law of non-contradiction is also found in inferences. On it are based, for example, direct inferences through the transformation of judgments. This operation is possible only because the object of thought cannot both belong and not belong to the same class of objects. Otherwise, there will be a logical contradiction. In inferences through the ratio of judgments in a logical square, the law of non-contradiction affects the fact that if any judgment is true, then the one that contradicts or opposes it will be false. In other words, they cannot both be true.
Finally, the law of contradiction operates in the proof. It underlies one of the rules of the grounds of evidence: they must not contradict each other. Without the operation of this law, refutation would be impossible. Having proved the truth of one thesis, it is not possible to conclude the falsity of the opposite or contradictory thesis.
The requirement of consistency of thought and its violation in the practice of thinking. The action of the objective law of non-contradiction in thinking makes an important requirement for a person - consistency in his reasoning, in the connections between thoughts. For our thoughts to be true, they must be consistent, consistent. Or: in the process of any reasoning, one cannot contradict oneself, reject one's own statements, recognized as true.
A variety of logical errors - "logical contradictions" - are associated with violation of the requirements of the law of non-contradiction.
The meaning of the law of non-contradiction. It is especially important to take into account the operation of the law of contradiction in science, since any scientific reasoning - more or less thorough, detailed, mutually exclusive thoughts can be in its different places and they are simply difficult to detect. It is all the more difficult to do this if the reasoning is divided in time: what was affirmed at one time may imperceptibly for the speaker himself be denied at another. But from this logical contradictions do not lose their harm. They are intellectual "slag" that clogs our reasoning and requires constant purification so that we can successfully move towards the truth. That is why science attaches fundamental importance to the prevention or elimination of logical contradictions in it.
One of the most important conditions for constructing a scientific system is the consistency of the initial data ("consistency of the system of axioms").
Another condition is the consistency of the theoretical constructions arising from them (“the consistency of the theoretical system itself”). If any contradiction of a logical order is found in science, then they try in every possible way to eliminate it, as an obstacle to the knowledge of the truth.
Logical contradictions are intolerable in everyday speech. A person is no longer respected if, on the same occasion, he says one thing today and another tomorrow. This is a man without principles.
3.4. The Law of the Excluded Middle and Its Importance in Determining TruthLaw of the excluded middle makes stronger demands on judgments and requires not to shy away from recognizing the truth of one of the contradictory statements and not to look for something third between them.
The law of the excluded middle is denoted by the formula A is either B or not B. The meaning of this formula is as follows. Whatever the object of our thought (A), this object either possesses a certain property (B) or does not possess it. It is impossible that it is false both that an object A has property B and that an object does not have this property. Truth is necessarily found in one of two contradictory propositions. No third judgment about the relation of A to B and not to B can be true. Therefore, there is a dichotomy here, according to which, if one of the two is true, then the other is false, and vice versa.
This law and its action is not reducible to the future, where the event will either take place or not. The law is alternative in the characterization of things, hypotheses and ways of solving problems, it requires different approaches to be distinguished and the true one to be determined.
The law of the excluded middle and the law of non-contradiction are related. Both of them do not allow the existence of conflicting thoughts. But there are also differences between them. The law of non-contradiction expresses the relationship between opposing propositions. For example: "This paper is white." “This paper is black.” The Law of the Excluded Middle expresses the relationship between conflicting propositions. For example: "This paper is white." “This paper is not white.” Because of this, in the case of the law of non-contradiction, both judgments cannot be simultaneously true, but they can be simultaneously false, and the third judgment will be true - "This paper is red." In the case of the operation of the law of the excluded middle, both judgments cannot be simultaneously false, one of them will necessarily be true, the other false, and no third, middle judgment is possible. If, on the other hand, judgments that are contradictory in form do not relate to a single object, but to a class of objects, when something is affirmed or denied regarding each object of a given class, and the same is denied regarding each object of a given class, then the truth relations between them are established according to the rules of “logical square." When one of the judgments affirms something about the whole class of objects or phenomena, and another judgment denies the same about a part of the objects or phenomena of the same class, then one of such judgments will necessarily be true, the other will be false, and the third is not given. For example: “All fish breathe with gills” and “Some fish do not breathe with gills.” Both of these propositions cannot be both true and false at the same time.
Requirements of the law of the excluded middle and their violations. Based on this law, certain requirements for thinking can be formulated. A person often faces a dilemma: to choose not from the same, but from mutually negating statements. The Law of the Excluded Middle just requires a choice - one of two - according to the principle "either - or", tetrium non datur (the third is not given). It means that when solving an alternative question, one cannot evade a definite answer; you can not look for something intermediate, middle, third.
Meaning of the Law of the Excluded Middle. This law cannot specify exactly which of the two contradictory propositions is true. But its significance lies in the fact that it establishes for us well-defined intellectual boundaries in which the search for truth is possible. This truth is contained in one of two contradictory statements. Beyond these limits, it makes no sense to look for it. The very choice of one of the judgments as true is ensured by the means of one or another science and practice.
Logic as the science of thinking. Subject and object of logic.
1. The word "logic" comes from the Greek logos, which means "thought", "word", "reason", "regularity". AT modern language This word is used, as a rule, in three meanings:
1) to denote patterns and relationships between events or actions of people in the objective world; in this sense one often speaks of the "logic of facts", "logic of things", "logic of events", "logic of international relations", "logic of political struggle", etc.;
2) to indicate the rigor, consistency, patterns of the thinking process; in this case, the following expressions are used: “logic of thinking”, “logic of reasoning”, “iron logic of reasoning”, “there is no logic in the conclusion”, etc.
3) to designate a special science that studies logical forms, operations with them and the laws of thought.
object logic as a science is human thinking. Subject logics are logical forms, operations with them and laws of thought.
2. The concept of a logical law. Laws and forms of thinking.
Logical law (law of thinking)- a necessary, essential connection of thoughts in the process of reasoning.
The law of identity. Every statement is identical to itself: A = A
The law of non-contradiction. A statement cannot be both true and false at the same time. If the statement BUT is true, then its negation not A must be false. Therefore, the logical product of a proposition and its negation must be false: A&A=0
Law of the excluded middle. A statement can be either true or false, there is no middle ground. This means that the result of the logical addition of the statement and its negation always takes the value true: A v A = 1
Law of sufficient reason- the law of logic, which is formulated as follows: in order to be considered completely reliable, any provision must be proven, that is, sufficient grounds must be known, by virtue of which it is considered true.
There are three main forms of thinking: concept, judgment and inference.
A concept is a form of thinking that reflects the general and, moreover, essential properties of objects and phenomena.
Judgment - this is a form of thinking that contains the assertion or denial of any position regarding objects, phenomena or their properties.
inference - such a form of thinking, in the process of which a person, comparing and analyzing various judgments, derives a new judgment from them.
The formation of the science of logic, the stages of its development.
| Stage 1 - Aristotle. He tried to find an answer to the question: "How do we reason." He analyzed human thinking, its forms - the concept, judgments, conclusions. This is how formal logic arose - the science of the laws and forms of thinking. | ARISTOTLE (lat. Aristotle(384-322 BC), ancient Greek scientist, philosopher |
| Stage 2 - the emergence of mathematical or symbolic logic. Its foundations were laid by the German scientist Gottfried Wilhelm Leibniz. He made an attempt to replace simple reasoning with actions with signs. |  Gottfried Wilhelm Leibniz (1646-1716) German philosopher, mathematician, physicist, linguist. |
| Stage 3 - the Englishman George Boole finally developed this idea, he was the founder of mathematical logic. In his works, logic acquired its own alphabet, spelling and grammar. The initial section of mathematical logic was called the algebra of logic or Boolean algebra. |  George Boole (1815-1864). English mathematician and logician. |
| George von Neumann laid the basis for the operation of a computer with a mathematical apparatus that uses the laws of mathematical logic. |
An example of expanding the scope of a concept with a simultaneous decrease in content
Moscow State University → State University→ University → Higher education institution → Educational (educational) institution → Educational institution → Institution → Organization → Subject of public law → Subject of law
The law is applicable only when the volume of one concept enters the volume of another, for example: "animal" - "dog". The law does not work for mismatched concepts, for example: "book" - "doll".
Reducing the scope of a concept with the addition of new features (that is, expanding the content) does not always occur, but only when the feature is characteristic of a part of the scope of the original concept.
Types of concepts.
Concepts are usually divided into the following types: 1) singular and general, 2) collective and non-collective, 3) concrete and abstract, 4) positive and negative, 5) irrelative and correlative.
1. Concepts are divided into singular and general, depending on whether one element or many elements are thought of in them. The concept in which one element is thought is called a single one (for example, “Moscow”, “L.N. Tolstoy”, “Russian Federation”). A concept in which a set of elements is conceived is called a general one (for example, "capital", "writer", "federation").
General concept, referring to an indefinite number of elements, is called non-registering. So, in the concepts of “man”, “investigator”, “decree”, a lot of elements conceivable in them cannot be taken into account: all people, investigators, decrees of the past, present and future are conceived in them. Non-registering concepts have an infinite scope.
2. Concepts are divided into collective and non-collective.
Concepts in which the signs of a certain set of elements that make up a single whole are thought are called collective. For example, "team", "regiment", "constellation". These concepts reflect a multitude of elements (team members, soldiers and regimental commanders, stars), but this multitude is conceived as a single whole. The content of a collective concept cannot be attributed to each individual element included in its scope, it refers to the entire set of elements. For example, the essential features of a team (a group of people united by a common work, common interests) are not applicable to each individual member of the team.
The concept in which the signs relating to each of its elements are thought is called non-collective. Such, for example, are the concepts of "star", "commander of the regiment", "state".
3. Concepts are divided into concrete and abstract, depending on what they reflect: an object (a class of objects) or its attribute (relationship between objects).
A concept in which an object or a set of objects is conceived as something independently existing is called concrete; a concept in which an attribute of an object or a relationship between objects is conceived is called abstract. Thus, the concepts of "book", "witness", "state" are concrete; the concepts of "whiteness", "courage", "responsibility" - abstract.
4. Concepts are divided into positive and negative, depending on whether their content consists of properties inherent in the object, or properties that are absent from it.
5. Concepts are divided into irrelative and correlative, depending on whether they conceive of objects that exist separately or in relation to other objects.
Concepts that reflect objects that exist separately and are thought outside their relationship to other objects are called irrelative. Such are the concepts of “student”, “state”, “crime scene”, etc.
To determine what kind a particular concept belongs to means to give it a logical description. So, giving a logical description of the concept of "Russian Federation", it is necessary to indicate that this concept is single, collective, concrete, positive, irrelevant. When characterizing the concept of "insanity", it should be indicated that it is general (non-registering), non-collective, abstract, negative, irrelevant.
6. Relations between concepts. +++++++++++
comparable concepts. According to the content, there can be two main types of relations between concepts - comparability and incomparability. In this case, the concepts themselves are respectively called comparable and incomparable.
Comparable concepts are divided into compatible and incompatible.
Compatibility relationships can be of three types. This includes equivalence, overlap and subordination.
Equivalence. The relation of equivalence is otherwise called the identity of concepts. It occurs between concepts containing the same subject. The volumes of these concepts coincide completely with different content. In these concepts, either one object or a class of objects containing more than one element is conceived. More simply, in relation to equivalence, there are concepts in which one and the same object is thought. As an example illustrating the relationship of equivalence, we can cite the concepts of "equilateral rectangle" and "square".
Crossing (crossing). The concepts that are in relation to the intersection are those whose volumes partially coincide. The volume of one is thus partly included in the volume of the other and vice versa. The content of such concepts will be different. A schematic representation of the intersection relationship is in the form of two partially aligned circles (Fig. 2). The point of intersection on the diagram is hatched for convenience. An example is the concepts of "peasant" and "tractor driver"; "mathematician" and "tutor".
Subordination (subordination). The relationship of subordination is characterized by the fact that the scope of one concept is completely included in the scope of another, but does not exhaust it, but is only a part.
Incompatibility relations are usually divided into three types, among which there are subordination, opposition and contradiction.
Subordination. The relationship of subordination arises when several concepts are considered that exclude each other, but at the same time have subordination to another, common to them, wider (generic) concept.
Opposite (contrast). Concepts that are in relation to the opposite can be called such species of the same genus, the contents of each of which reflect certain features that are not only mutually exclusive, but also replace each other.
Contradiction (contradiction). The relation of contradiction arises between two concepts, one of which contains certain features, and the other denies (excludes) these features without replacing them with others.
Comparable- these are concepts that somehow have in their content common essential features (by which they are compared - hence the name of their relationship). For example, the concepts of "law" and "morality" contain a common feature - "social phenomenon".
incomparable concepts. Incomparable- concepts that do not have any significant common features in one way or another: for example, "law" and "universal gravitation", "right" and "diagonal", "right" and "love".
True, even such a division is to a certain extent conditional, relative, because the degree of incomparability can also be different. For example, what is there in common between such seemingly different concepts as “spaceship” and “fountain pen”, except for some purely external similarity in the form of the structure? And meanwhile, both are the creations of human genius. What is common between the concepts of "spy" and "letter b"? Like nothing. But here is the unexpected association they evoked in A. Pushkin: “Spies are like the letter Ъ. They are needed only in some cases, but even here you can do without them, and they are used to popping in everywhere. Hence, the common feature is "necessary sometimes."
There are incomparable concepts in any science. They also exist in legal science and practice: “alibi” and “pension fund”, “guilt” and “version”, “legal adviser” and “independence of the judge”, etc., etc. Incomparability characterizes even, it would seem, , similar in content concepts: "enterprise" and "administration of the enterprise", "labor dispute" - "consideration of a labor dispute" and "body for considering a labor dispute", "collective agreement" and "collective negotiations on a collective agreement". It is important to take this circumstance into account in the process of operating with such concepts, so as not to fall into a comical situation, despite the desire.
Classification of judgments.
The predicate of the judgment, which will be the bearer of novelty, may have a very different character. From this point of view, in all the variety of judgments, there are three most common groups: attributive, relational and existential.
Attribute judgments(from Lat. altributum - property, sign), or judgments about the properties of something, reveal the presence or absence of certain properties (or signs) in the subject of thought. For example: "All republics former USSR declared their independence”; "The Commonwealth of Independent States (CIS) is fragile." Since the concept that expresses the predicate has content and scope, attributive judgments can be considered in two ways: content and volume.
Relational judgments(from lat. relatio - relation), or judgments about the relationship of something to something, reveal the presence or absence of an object of thought of one or another relationship to another object (or several objects). Therefore, they are usually expressed by a special formula: x R y, where x and y are objects of thought, and R (from relatio) is the relationship between them. For example: "CIS is not equal to the USSR", "Moscow is bigger than St. Petersburg".
Examples. The proposition "All metals are electrically conductive" can be turned into the proposition "All metals are like electrically conductive bodies." In turn, the judgment “Ryazan is smaller than Moscow” can be turned into the judgment “Ryazan belongs to the cities that are smaller than Moscow”. Or: "Knowledge is what is like money." In modern logic there is a tendency to reduce relational judgments to attributive ones.
Existential judgments(from Latin existentia - existence), or judgments about the existence of something, these are those in which the presence or absence of the very subject of thought is revealed. The predicate here is expressed by the words “exists” (“does not exist”), “is” (“no”), “was” (“was not”), “will be” (“will not be”), etc. For example: “Smoke without there is no fire”, “CIS exists”, “ Soviet Union No". In the process of legal proceedings, first of all, the question is decided whether the event took place: “There is a crime” (“There is no evidence”).
The quality of the bond
The quality of judgment is one of its most important logical characteristics. By it is meant not the actual content of the judgment, but its most general logical form - affirmative, negative or negating. This shows the deepest essence of any judgment in general - its ability to reveal the presence or absence of certain connections and relations between conceivable objects. And this quality is determined by the nature of the bundle - “is” or “is not”. Depending on this, simple judgments are divided according to the nature of the link (or its quality) into affirmative, negative and negative.
In affirmative judgments reveals the existence of any connection between the subject and the predicate. This is expressed by means of the affirmative connective “is” or the words corresponding to it, a dash, the agreement of words. The general formula for an affirmative judgment is "S is P". For example: "Whales are mammals."
In negative Judgments, on the contrary, reveal the absence of one or another connection between the subject and the predicate. And this is achieved with the help of the negative link "is not" or the words corresponding to it, as well as simply by the particle "not". The general formula is "S is not P". For example: "Whales are not fish." At the same time, it is important to emphasize that the particle “not” in negative judgments certainly stands before the copula or is implied. If it is after the link and is part of the predicate (or subject) itself, then such a judgment will still be affirmative. For example: “It is not false freedom that lives in my poems.”
negative judgments- these are judgments in which the nature of the bundle is double. For example: “It is not true that a person will never leave solar system».
By volume of the subject
In addition to the initial, fundamental division of simple, categorical judgments according to quality, there is also their division according to quantity.
The amount of judgment is its other most important logical characteristic. Quantity here means by no means any specific number of objects conceivable in it (for example, the number of days of the week, months or seasons, planets of the solar system, etc.), but the nature of the subject, i.e. its logical scope. Depending on this, general, particular and singular judgments are distinguished.
General judgments have their own varieties. First of all, they can be selective and non-selective.
Particular judgments are those in which something is said about a part of a group of objects. In Russian, they are expressed by such words as “some”, “not all”, “most”, “part”, “separate”, etc. In modern logic, they are called the “existence quantifier” and are denoted by the symbol “$” (from English exist - to exist). The formula $ x P(x) reads: "There is x such that property P(x) holds." AT traditional logic adopted the following formula of private judgments "Some S is (is not) P".
Examples: "Some wars are fair", "Some wars are unfair" or "Some witnesses are truthful", "Some witnesses are not truthful". The quantifier word can also be omitted here. Therefore, in order to determine whether there is a particular or general judgment, one must mentally substitute the appropriate word. For example, the proverb “To err is human” does not mean that this applies to every person. Here the concept of "people" is taken in a collective sense.
By modality
The main informative function of judgment as a form of thinking is reflection in the form of affirmation or denial of the connections between objects and their features. This applies to both simple and complex judgments, in which the presence or absence of a connection is complicated by connectives.
The modality of judgments is additional information expressed in the judgment in an explicit or implicit form about the nature of the validity of the judgment or the type of relationship between the subject and the predicate, reflecting the objective relationship between objects and their attributes.
Compound sentences and their types.
Complex propositions are formed from several simple propositions. Such, for example, is the statement of Cicero: “After all, even if acquaintance with law represented an enormous difficulty, even then the consciousness of its great usefulness should have encouraged people to overcome this difficulty.”
Just like simple propositions, complex propositions can be true or false. But unlike simple judgments, the truth or falsity of which is determined by their correspondence or non-correspondence to reality, the truth or falsity of a complex judgment depends primarily on the truth or falsity of its constituent judgments.
The logical structure of complex judgments also differs from the structure of simple judgments. The main structure-forming elements here are no longer concepts, but simple judgments that make up a complex judgment. At the same time, the connection between them is carried out not with the help of ligaments “is”, “is not”, etc., but through the logical unions “and”, “or”, “or”, “if [...], then” and others. Legal practice is especially rich in such judgments.
In accordance with the functions of logical connectives, complex judgments are divided into the following types.
1 Connective judgments (conjunctive) are such judgments that include as constituent parts other judgments are conjuncts, united by a bunch of "and". For example, "The exercise of the rights and freedoms of man and citizen must not violate the rights and freedoms of other persons."
2 Disjunctive (disjunctive) judgments - include as components of the judgment - disjuncts united by the link "or". For example, "The plaintiff has the right to increase or decrease the size of the claims."
There is a weak disjunction, when the union “or” has a connecting-separating meaning, that is, the components included in a complex proposition do not exclude each other. For example, "A contract of sale may be concluded orally or in writing." Strong disjunction occurs, as a rule, when the logical unions “or”, “or” are used in an exclusive-separating sense, that is, its components exclude each other. For example, “Slander, combined with the accusation of a person of committing a grave or especially grave crime, is punishable by restriction of liberty for a term of up to three years, or by arrest for a term of four to six months, or by imprisonment for a term of up to three years.”
Conditional (implicative) propositions are formed from two simple propositions through the logical union "if [...], then". For example, "If after the expiration of the period of temporary work with the employee the contract was not terminated, then he is considered accepted for permanent work." The argument that begins in implicative judgments with the word "if" is called the basis, and the component that begins with the word "then" is called the consequence.
Conditional propositions primarily reflect objective causal, spatio-temporal, functional and other relationships between objects and phenomena of reality. However, in the practice of applying legislation, the rights and obligations of people associated with certain conditions can also be expressed in the form of an implication. For example, "Soldiers of military units Russian Federation located outside the Russian Federation, for crimes committed on the territory of a foreign state, are criminally liable under this Code, unless otherwise provided by an international treaty of the Russian Federation ”(Clause 2, Article 12 of the Criminal Code of the Russian Federation).
At the same time, it must be borne in mind that the grammatical form “if [...], then” is not an exclusive feature conditional proposition, it can express a simple sequence. For example, “If the person who directly committed the crime is recognized as the perpetrator, then the instigator is the person who persuaded another person to commit
Types of questions.
Questions can be classified in various ways. Consider the main types of issues that are most often addressed in the legal field.
1. According to the degree of expression in the text, questions can be explicit and hidden. An explicit question is expressed in language in its entirety, along with its presuppositions and the requirement to ascertain the unknown. The hidden question is expressed only by its premises, and the requirement to eliminate the unknown is restored after understanding the premises of the question. For example, if we read the text: “More and more ordinary citizens become owners of shares, and sooner or later the day comes when there is a desire to sell them”, we will not find clearly formulated questions here. However, when comprehending what you read, you may want to ask: “What is a share?”, “Why should they be sold?”, “How to sell shares correctly?” etc. The text thus contains hidden questions.
2. According to their structure, questions are divided into simple and complex. A simple question structurally involves only one judgment. It cannot be broken down into elementary questions. A complex question is formed from simple ones with the help of logical unions “and”, “or”, “if, then”, etc. For example, “Which of those present identified the criminal, and how did he react to this?”. When answering a complex question, it is preferable to break it down into simpler questions. Question like: “If the weather is fine, will we go on an excursion?” - does not apply to complex questions, since it cannot be divided into two independent simple questions. This is an example of a simple question. The meaning of conjunctions forming complex questions is thus not identical with the meaning of the corresponding logical conjunctions by which complex true or false propositions are formed from simple true or false propositions. Questions are not true or false. They may be right or wrong.
3. According to the method of requesting the unknown, clarifying and supplementing questions are distinguished. Clarifying questions (or "whether" - questions) are aimed at revealing the truth of the judgments expressed in them. In all these questions, there is a particle “whether”, included in the phrases “is it true”, “is it really”, “is it necessary”, etc. For example, “Is it true that Semenov successfully defended thesis?”, “Is there really more people in Moscow than in Paris?”, “Is it true that if he passes all the exams with excellent marks, he will receive an increased scholarship?” and others. Complementary questions (or “to” - questions) are designed to identify new properties of the object under study, to obtain new information. A grammatical sign is an interrogative word like “Who?”, “What?”, “Why?”, “When ?", "Where?" etc. For example, “How to conclude an agreement for the provision of brokerage services?”, “When was this traffic accident committed?”, “What does the word “sponsor” mean?” and etc
4. According to the number of possible answers, questions are open and closed. An open question is a question that has an indefinite set of answers. A closed question is a question that has a finite, most often quite limited, number of answers. These questions are widely used in judicial and investigative practice, in sociological research. For example, the question “How does this teacher lecture?” is an open question, as many answers can be given to it. It can be restructured in order to “close”: “How does this teacher lecture (good, satisfactory, bad)?”.
5. In relation to the cognitive goal, questions can be divided into key and suggestive. A question is a key question if the correct answer to it serves directly to achieve the goal. The question is leading if the correct answer somehow prepares or brings the person closer to understanding the key question, which, as a rule, turns out to be dependent on the illumination of leading questions. Obviously, there is no clear boundary between key and leading questions.
6. According to the correctness of the formulation of questions, they are divided into correct and incorrect. Correct (from lat. correctus - polite, tactful, courteous) question is a question, the premise of which is true and consistent knowledge. An incorrect question is based on the premise of a false or contradictory judgment, or a judgment whose meaning is not defined. There are two types of logically incorrect questions: trivially incorrect and non-trivially incorrect (from Latin trivialis - hackneyed, vulgar, devoid of freshness and originality). A question is trivially incorrect, or meaningless, if it is expressed in sentences containing obscure (indefinite) words or phrases. An example is the following question: "Does critical metaphysication by abstractions and discrediting the tendency of cerebral subjectivism lead to ignoring the system of paradoxical illusions?"
Types of responses.
Among the answers, there are: 1) true and false; 2) direct and indirect; 3) short and detailed; 4) complete and incomplete; 5) exact (certain) and inaccurate (indefinite).
1. True and false answers. By semantic status, i.e. in relation to reality, answers can be true or false. The answer is regarded as true if the judgment expressed in it is correct, or adequately reflects reality. The answer is regarded as false if the judgment expressed in it is incorrect, or does not adequately reflect the state of affairs in reality.
2. Answers direct and indirect. These are two types of answers, differing in the scope of their search.
A direct answer is one that is taken directly from the search for answers, in the construction of which additional information and reasoning are not used. For example, a direct answer to the question “In what year did the Russo-Japanese War end?” there will be a judgment: "The Russo-Japanese War ended in 1904." A direct answer to the Li-question "Is a whale a fish?" there will be a judgment: "No, the whale is not a fish."
An indirect answer is a response that is obtained from a wider area than the area of response search, and from which only the necessary information can be obtained by inference. So, for the question "In what year did the Russo-Japanese war end?" the following answer will be indirect: "The Russo-Japanese War ended one year before the First Russian Revolution." To the question "Is a whale a fish?" the answer will be indirect: "The whale belongs to mammals."
3. Short and detailed answers. In grammatical form, answers can be short and detailed.
Short - these are monosyllabic affirmative or negative answers: "yes" or "no".
Expanded - these are answers, in each of which all elements of the question are repeated. For example, to the question "Was JFK a Catholic?" affirmative answers can be received: short - "Yes"; expanded - "Yes, J. Kennedy was a Catholic." Negative answers will be: short - "No"; extended - "No, JFK was not a Catholic."
Short answers are usually given to simple questions; for complex questions, it is advisable to use detailed answers, since monosyllabic answers in this case often turn out to be ambiguous.
4. Complete and incomplete answers. According to the amount of information provided in the answer, the answers may be complete or incomplete. The problem of completeness most often arises when answering complex questions.
A complete answer includes information on all elements or parts of the question. For example, to the difficult question "Is it true that Ivanov, Petrov and Sidorov are accomplices in the crime?" the following answer will be complete: "Ivanov and Sidorov are accomplices in the crime, and Petrov is the executor." To the difficult question “By whom, when and in connection with what was the poem “On the Death of a Poet” written?” the complete answer would be:
“The poem “On the Death of a Poet” was written by M.Yu. Lermontov in 1837 in connection with the tragic death of A.S. Pushkin.
An incomplete answer includes information about individual elements or sub-parts of the question. So, to the above question "Is it true that Ivanov, Petrov and Sidorov are accomplices in the crime?" - the answer will be incomplete: "No, it's not true, Petrov is the performer."
5. Accurate (definite) and inaccurate (uncertain) answers! The logical relationship between the question and the answer means that the quality of the answer is largely determined by the quality of the question. It is no coincidence that in polemics and in the process of interrogation the rule applies: what is the question, such is the answer. This means that it is difficult to get a clear answer to a vague and ambiguous question; If you want to get a precise and definite answer, then formulate a precise and definite question.
Types of dilemmas
Conditional disjunctive inferences are inferences in which one of the premises is a disjunctive statement, and the rest are conditional statements. Another name for conditionally divisive inferences is lemmatic, which comes from the Greek word lemma - a sentence, an assumption. This name is based on the fact that these inferences consider various assumptions and their consequences. Depending on the number of conditional premises, conditionally divisive conclusions are called dilemmas (two conditional premises), trilemmas (three), polylemmas (four or more). In the practice of reasoning, dilemmas are most often used.
The following main types of dilemmas can be distinguished:
- a simple design dilemma,
– complex design dilemma,
- a simple destructive dilemma,
is a complex destructive dilemma.
An example of a simple constructive dilemma (Socrates' reasoning):
“If death is a transition into non-existence, then it is good. If death is a transition to another world, then it is good. Death is a transition to non-existence or to another world. Therefore, death is a blessing.
A simple constructive (affirmative) dilemma:
If A, then C.
If B, then C.
An example of a complex design dilemma:
A young Athenian turned to Socrates for advice: should he marry? Socrates replied: “If you get a good wife, then you will be a happy exception, if a bad one, then you will be like me, a philosopher. But you will get a good or a bad wife. Therefore, either you be a happy exception, or a philosopher.
Difficult design dilemma:
If A, then B.
If C, then D.
An example of a simple destructive dilemma:
"AT modern world if you want to be happy, you need to have a lot of money. However, it has always been the case that if you want to be happy, you need to have a clear conscience. But we know that life is arranged in such a way that it is impossible to have both money and conscience at the same time; or no money, or no conscience. Therefore, give up hope for happiness.”
A simple destructive (denying) dilemma:
If A, then B.
If A, then C.
False B or False C.
False A.
An example of a complex destructive dilemma:
“If he is smart, he will see his mistake. If he is sincere, he will confess it. But he either does not see his mistake, or does not admit it. Therefore, he is either not smart or not sincere.
Difficult destructive dilemma:
If A, then B.
If C, then D.
Not-B or Not-D.
Not-A or Not-C.
An example of a complete inductive inference.
All guilty verdicts are issued in a special procedural order.
All acquittals are issued in a special procedural order.
Guilty verdicts and acquittals are decisions of the court.
All court decisions are issued in a special procedural order.
This example reflects the class of objects - court decisions. All (both) of its elements were specified. Right side each of the premises is valid with respect to the left. Therefore, the general conclusion, which is directly related to each case separately, is objective and true.
Incomplete induction called a conclusion, which, on the basis of the presence of certain recurring features, ranks this or that object in the class of objects homogeneous to it, which also have such a feature.
Incomplete induction is often used in daily human life and scientific activity, as it allows to draw a conclusion based on the analysis of a certain part of a given class of objects, saves time and human effort. At the same time, we must not forget that as a result of incomplete induction, a probabilistic conclusion is obtained, which, depending on the type of incomplete induction, will fluctuate from less probable to more probable (11) .
The above can be illustrated by the following example.
The word "milk" changes by case. The word "library" changes by case. The word "doctor" changes by case. The word "ink" changes by case.
The words "milk", "library", "doctor", "ink" are nouns.
Probably all nouns change in cases.
Depending on that
Logics is the science of thought. The founder of science Aristotle.
Logics- the science of the laws and forms of human thinking, considered as a means of knowing the surrounding reality.
To clarify the subject of logic, you can use several methods, each of which gives a certain-result. First method– etymological. It lies in the fact that it is required to clarify the meaning of the word that is used to name this science. The term "logic" goes back to the ancient Greek word "logos", meaning word, thought, concept, reasoning and law. The etymology of the word "logic" shows that this is a science related to human thinking, substantiates reasoning with the help of foundations, which later became known as logical laws. The disadvantage of this method is the ambiguity of the word "logic". In everyday life, in popular, general scientific and philosophical literature, this word is used in a wide range of meanings. Ratings "logical" and "illogical" can be used to characterize human actions, evaluate events, etc. Second method– reference and academic. It lies in the fact that we are looking for the answer to the question in dictionaries and encyclopedias. In most dictionaries and textbooks, logic is defined as the science of the laws and forms of correct thinking, and the subject of this science is human thinking. However, logic considers not only correct thinking, but also errors that arise in the process of thinking: paradoxes, etc.
Subject of logic- human thinking. The very term "thinking" is quite broad and does not make it possible to determine the specifics of logic in relation to other sciences.
Logic value consists of the following:
1) logic is the most important means of forming beliefs (primarily scientific).
2) formal logic is used in science and technology.
3) traditional formal logic remains the most important tool in the field of all types of education. It is the basis for organizing all types of knowledge for its presentation in the learning process;
4) logic is the most important and indispensable tool for the development of culture. No cultural activity in general can do without logic, since rational elements are present and play a fundamental role in it.
2. Forms of thought
The forms of thinking are: concept, judgment, conclusion.
Thinking begins with the forms of sensory knowledge of the world - sensations, perception, representation.
Thinking- this is the highest reflection of being in relation to the sensual form.
concept- this is a logical thought about any subject with a certain set of essential features.
Judgment - it is a form of thinking, in which something is affirmed or denied about the surrounding world, objects, phenomena, as well as relations and connections between them.
inference- this is a form of abstract thinking, through which new information is derived from previously available information. In this case, the sense organs are not involved, i.e. the whole process of inference takes place at the level of thinking and is independent of the information received at the moment from the outside.
