And the laws to which thinking is subject.
Logic studies not the specific content of reality, but thoughts about it, their structure, what is common to thoughts of a given type, regardless of their specific content. Therefore, when studying logic, in order to understand the essence of the thinking process, the specific content of forms and laws, you need to be able to generalize specific reasoning, be able to operate with the resulting formulas and diagrams. The main goal of studying logic comes down to acquiring the skills of conscious application of logical rules and laws to the real process of thinking.
Logic is an internal pattern inherent in certain phenomena; correct, reasonable line of reasoning. Various processes have their own internal logic; in this regard, they talk about the logic of emotions, the logic of decision making. At the same time, logic as a science examines how others can be deduced from some statements. Knowledge of logic allows us to analyze our reasoning, helps to determine their consistency, consistency, evidence, and thereby determine true statements from false ones.
In life, logic is not so much the rules of thinking as the rules for formatting thoughts in the form of text.
Since you can look at the same object from different angles and see different things, then different ways reasonable reasoning - a lot. There is not one logic, there are many different logics. There is formal logic, there is informal (life) logic, there is dialectical logic, there is feminine logic, and there is the logic of scientific proof.
Thus, John Stuart Mill formulated Mill's Canons as "an agreed view of the principles of proof and methods scientific research". Five canons (rules or laws) are formulated as the "regulatory principles" of these experimental methods: the method of similarity, the method of difference, the combined method of similarity and difference, the method of residues and the method of concomitant changes. These canons prescribe methods for the discovery and evidential justification of causal laws and causal connections See →
Should logic be taught?
After the war in the USSR, logic was taught in secondary schools for 10-12 years. It is interesting that logic was a compulsory subject in the same years as psychology: on December 3, 1946, the Central Committee of the All-Union Communist Party of Bolsheviks, in its resolution “On the teaching of logic and psychology in secondary schools,” recognized that it was completely abnormal that logic and psychology were not studied in secondary schools , and considered it necessary to introduce, within 4 years, starting from the 1947/48 academic year, the teaching of these subjects in all schools Soviet Union. In 1959, the teaching of logic in secondary schools was abolished. But in vain. For those interested, here is a link to Vinogradov’s famous logic textbook from 1954.
At the same time, it is important to understand that logic is not synonymous with rationality: logical people sometimes do not do the most reasonable things when they cannot look at the situation broadly enough or they fail to identify all that is important and significant in what is happening. Gaining life experience and education, people one way or another master logic, but they do not always use it and their logic does not always rise to the level of wisdom.
A person in everyday life and in professional activity constantly learns about the world around him, himself and the people around him, acquiring various types of knowledge.
Knowledge - this is information, information received by the subject, processed by him on the basis personal experience or social practice and serving him as regulators of his cognitive-transformative activity.
The subject does this through sensory cognition and abstract thinking. Through sensory reflection (sensations, perceptions, ideas), based on mental processes, a person cognizes individual objects and their properties.
Feeling - the simplest mental process of reflecting individual properties of objects and internal states of the body that arise when direct impact material stimuli to the senses.
About “Topic”, “Categories”, “On the refutation of sophistic arguments”, “On interpretation”. Byzantine logicians united all of the listed works of Aristotle under the common name “Organon” (Instrument of Knowledge). - Cm.: Aristotle. Op. T. 2. M., 1978.
Perception - This is the process of reflecting objects and phenomena of the objective world that are currently affecting human analyzers.
Performance - This is a process of visual and generalized reflection of objects and phenomena (or their individual properties) that do not currently affect our senses.
Sensory reflection is the basis of abstract thinking, which allows us to cognize the laws of the world and the essence of objects. Abstract, or rational, thinking reflects the world and its processes deeper and more fully than sensory thinking.
People always reason, trying to extract new ones from the knowledge they have. Knowledge obtained in this way is called inferential. The process of generating inferential knowledge naturally obeys certain logical laws.
The main purpose of logic is precisely to explore specific mental laws and develop rules for obtaining inferential knowledge.
Consequently, the object of logic as a science is human thinking.
But thinking is a complex, multifaceted process, the highest form of knowledge of the world, characteristic only of man. And not everyone is interested in logic here. The essence of thinking, its origin, relationship to the world and its cognitive capabilities is studied by philosophy. Physiology is interested in how thinking depends on the state of the brain, the material substrate of thought. Psychology studies the conditions for the optimal development and functioning of thinking, the influence of the socio-psychological environment and feelings on it. Genetics is trying to reveal the secrets of children inheriting abilities for any activity from their parents. Cybernetics scientists are studying the technical possibilities of modeling human thinking on a computer with flexible feedback.
Logic does not delve into the content of thoughts, since it is obvious that in this parameter the thoughts of a mathematician differ from the thoughts of a biologist, a musician thinks about something completely different from a judge, a scientist uses concepts and terms in research that are not at all used in everyday thinking and language. And what can a person talk about!
However, in many thoughts that are completely different in content, one can find something essentially common. This is their structure or shape. Logic, studying the structure of thoughts in abstraction from their specific content, establishes laws and rules of reasoning that lead from one true statement to another. Main types forms, in which thoughts are expressed, are: concept, judgment, theory etc. The main types of forms in which knowledge development occurs are: inference, hypothesis, solution, version, task, problem and etc.
Characteristic of thinking is the fact that knowledge of reality and the development of knowledge are carried out in a generalized, indirect manner.
Generalized, because in thoughts and concepts a person reflects the aspects of objects and phenomena that interest him, abstracting from the rest, and our concepts reflect the signs not only of a given individual object and phenomenon, but also the signs of content inherent in many objects and phenomena of a given class. So, when we use the concept of “judge”, we mean a whole class of representatives of the judiciary. For example, not only the specific Chairman of the Constitutional Court of the Russian Federation, but also the general characteristics of judges of the past, present and future.
Indirectly, because thinking allows us to gain new knowledge about the world, not each time directly turning to experience, but relying on previous knowledge. If we know with certainty that the judiciary always protects the rights of citizens, then using this thought as an initial judgment, we can obtain a new true statement: “Courts in Russian Federation also protect the rights of Russian citizens.”
The main purpose of logic is precisely to study the specific laws of thinking, to develop not only the rules for achieving true inferential knowledge, but also to determine the ways, means and forms of implementing this process.
Thus, we can define logic as a science.
Logics(from Greek Aouo
The subject of logic as a science is these are forms and means of thought, the laws of correct thinking and obtaining inferential knowledge, as well as methods of reasoning and formulating true conclusions, generalizations, recommendations, and decisions.
Logic is sometimes called the science of correct thinking. This definition of logic, although it suffers from some vagueness, has a basis. Indeed, when they want to check the correctness of any reasoning, they turn to the laws and rules of logic. Logic helps us think in such a way as to reach true conclusions.
Since logic in the narrow sense is interested in shape constructing thoughts and is distracted from the specific information contained in them, it is called formal logic.
Distracting from the specific content of thoughts, logic does not neglect the question of whether the statements with which we operate in thinking are true or false. Depending on whether the original statements are true or false, the output can be true or false. Therefore, logic, in order to be a means of discovering truth, must, based on the study of formal structures of thinking, establish laws of dependence between true and false judgments.
For example, the following two propositions:
“Cato the Elder spoke about the need to destroy Carthage” and “Plevako - a cunning lawyer” - do not have the same content, but they have the same logical structure. In the first and second judgments, the object of thought is attributed some kind of a certain property. Schematically it will look like this: S is P, where: S is the subject of thought; (from lat. subjectum- subject, in a statement-judgment - logical subject); P is a property that is attributed to this object; (from lat. proedicatum - what is said in a statement-judgment is a predicate).
To substantiate our conclusion, consider two more arguments: “All astronauts are brave people. G. Titov - cosmonaut. Consequently, G. Titov is a brave man" and "All first-year students Russian Academy justice study logic. Tanya Petrova is a first-year student at the Russian Academy of Justice. Hence,
Tanya Petrova studies logic." The content of these arguments is different, but the logical structure (form) is the same. In logic it is often written like this:
The propositions “M is P” and “S is M” are related to each other by their common term “M” (the letter “M” denotes a concept that has the same content in the first and second statements. It is called the middle term (from lat. medium- average)) and thanks to this the conclusion is possible: “S is P.”
It turns out that formal logic or logic in a narrow sense is the science of connections, arising between the truth and falsity of any sentences in terms of their form, structures, especially about the connection between the following of some sentences from others.
The history of logic goes back more than 2.5 thousand years and is divided into two main stages. The first began with the works of Aristotle and continued until the beginning of the 20th century. The second is from that time to the present day. It is almost impossible to list all the outstanding thinkers who developed logic. A special course should be devoted to this issue. At the same time, you should pay attention to the fact that already in Ancient Greece Representatives of the “Stoic” school (Chrinsii) paid great attention to logic. One of the most prominent personalities in the logical culture of the Middle Ages is I. D. Scot. F. Bacon made a significant contribution to the development of formal logic as a science. He laid the foundation for the logical doctrine of induction, the purpose of which is to discover causal relationships between phenomena in the surrounding world through observations and experiments. J. S. Mill developed methods of scientific induction based on the establishment of causal relationships. G. Leibniz substantiated the idea of the possibility of presenting a proof as a mathematical calculation. D. Boole interpreted inference as the result of solving logical equalities. G. Frege used logic to study the foundations of mathematics. Significant contributions to the development of logic were subsequently made by B. Bolzano, O. De Morgan, W. S. Jevons, C. S. Pierce, E. Schroeder and others.
The beginning of the 20th century marks a kind of revolution in logic. Fundamental results were obtained by K. Gödel, D. Gilbert, B. Racel, A. Tarski, A. N. Whitehead, A. Church and others.
Our compatriots also made a great contribution to the development of logic. The evolution of logical ideas in Russia is associated with a brilliant constellation of names: these are the Likhud brothers, M.V. Lomonosov, P.S. Poretsky, N.A. Vasilyev, A.A. Markov-son, etc. In recent decades, much has been done for development of modern training course logicians were made by A. P. Alekseev, L. B. Bazhenov, V. A. Bocharov, E. K. Voishvillo, A. D. Getmanova, D. P. Gorsky, A. A. Ivin, Yu. V. Ivlev, V. I. Kirillov, S. A. Lebedev, V. I. Markin, A. L. Nikiforov, S. I. Povarnin, G. I. Ruzavin, P. Sergeich, V. I. Svintsov, A. A. Starchenko, M. K. Treushnikov, A. I. Uemov, etc.
- In contrast to dialectical logic, which in a certain sense coincides with the theory of knowledge.
Logics is the science of thinking. Founder of science Aristotle.
Logics– the science of the laws and forms of human thinking, considered as a means of understanding the surrounding reality.
To clarify the subject of logic, you can use several methods, each of which gives a specific result. First method– etymological. It lies in the fact that it is necessary 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 that substantiates reasoning using principles that 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. Assessments of “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 look for the answer to a 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 during the thinking process: paradoxes, etc.
Subject of logic- human thinking. The term “thinking” itself is quite broad and does not make it possible to determine the specifics of logic in relation to other sciences.
Logic value is as follows:
1) logic is the most important means of forming beliefs (primarily scientific ones).
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 thinking
Forms of thinking are: concept, judgment, inference.
Thinking begins with forms of sensory knowledge of the world - sensations, perception, representation.
Thinking– this is the highest reflection of existence in relation to the sensory form.
Concept- this is a logical thought about any object with a defined set of essential features.
Judgment – This is a form of thinking in which something is affirmed or denied about the surrounding world, objects, phenomena, as well as relationships and connections between them.
Inference is a form of abstract thinking through which new information is derived from previously existing information. In this case, the senses are not involved, i.e. the entire process of inference takes place at the level of thinking and is independent of information received from the outside at the moment.
LOGIC AS SCIENCE
1. Subject of logic
2. The emergence and development of logic
3. Language of logic
4. Forms and laws of thinking
1. Subject of logic
Keywords: logic, thinking, sensory cognition, abstract thinking.
Logic (from Greek: logos - word, concept, reason) is the science of the forms and laws of correct thinking. The mechanism of thinking is studied by a number of sciences: psychology, epistemology, cybernetics, etc. The subject of scientific logical analysis is the forms, techniques and laws of thinking with the help of which a person cognizes the world and myself. Thinking is the process of indirectly reflecting reality in the form of ideal images.
Forms and techniques of thinking that contribute to the knowledge of truth. A person acquires knowledge about the phenomena of the world in the process of active, purposeful cognition: the subject - the object interaction of a person with fragments of reality. Cognition is represented by several levels, a number of forms and techniques that lead the researcher to correct conclusions, when the truth of the initial knowledge presupposes the truth of the conclusions.
We know that the first level is sensory knowledge. It is carried out on the basis of the senses, their comprehension and synthesis. Let us recall the main forms of sensory knowledge:
1) sensation;
2) perception;
3) presentation.
This level of cognition has a number of important techniques, among which are the analysis and systematization of sensations, arranging impressions into a holistic image, memorization and recollection of previously acquired knowledge, imagination, etc. Sensory cognition provides knowledge about the external, individual properties and qualities of phenomena. Man strives to understand the deep properties and essences of things and phenomena, the laws of existence of the world and society. Therefore, he resorts to studying the problems that interest him at an abstract theoretical level. At this level, such forms of abstract cognition develop as:
a) concept;
b) judgment;
c) inference.
When resorting to these forms of cognition, a person is guided by such techniques as abstraction, generalization, abstraction from the particular, isolation of the essential, derivation of new knowledge from previously known, etc.
The difference between abstract thinking and sensory-figurative reflection and knowledge of the world. As a result of sensory cognition, a person develops knowledge obtained directly from experience in the form of ideal images based on sensations, experiences, impressions, etc. Abstract thinking marks the transition from the study of individual aspects of objects to the comprehension of laws, general connections and relationships. At this stage of cognition, fragments of reality are reproduced without direct contact with the sensory-objective world by replacing them with abstractions. Abstracting from a single object and temporary state, thinking is able to highlight in them the general and repetitive, essential and necessary.
Abstract thinking is inextricably linked with language. Language is the main means of fixing thoughts. Not only substantive meanings are expressed in linguistic form, but also logical ones. With the help of language, a person formulates, expresses and conveys thoughts, records knowledge.
It is important to understand that our thinking indirectly reflects reality: through a series of interconnected knowledge through logical sequences, it becomes possible to arrive at new knowledge without directly coming into contact with the objective-sensory world.
The importance of logic in cognition follows from the possibilities of deducing reliable knowledge not only by a formal-logical way, but also by a dialectical one.
The task of logical action is, first of all, to discover such rules and forms of thinking that, regardless of specific meanings, will always lead to true conclusions.
Logic studies the structures of thinking that lead to a consistent transition from one judgment to another and form a consistent system of reasoning. It performs an important methodological function. Its essence is to develop research programs and technologies suitable for obtaining objective knowledge. This helps equip a person with the basic means, methods and methods of scientific and theoretical knowledge.
The second main function of logic is analytical-critical, implementing which it acts as a means of detecting errors in reasoning and monitoring the correctness of thought construction.
Logic is also capable of performing epistemological tasks. Without stopping at the construction of formal connections and elements of thinking, logical knowledge is able to adequately explain the meaning and meaning of language expressions, express the relationship between the knowing subject and the cognitive object, and also reveal the logical-dialectical development of the objective world.
Tasks and exercises
1. The same cube, on the sides of which there are numbers (0, 1, 4, 5, 6, 8), is in three different positions.
| 0 |
| 4 |
| 0 |
| 4 |
| 5 |
1) Logic- In the book: 1) the universal boundary of the givenness of things in the world, which itself remains invisible; 2) a technique for indirectly identifying this boundary.
2) Logic- Activity can provide only one half of wisdom; the other half depends on perceptive inactivity. Ultimately, the debate between those who base logic on "truth" and those who base it on "research" stems from differences in values and at a certain point becomes meaningless. In logic it is a waste of time to consider conclusions concerning particular cases; we always deal with completely general and purely formal implications, leaving for other sciences the study of in which cases the assumptions are confirmed and in which they are not. Although we can no longer be content with defining logical statements as following from the law of contradiction, we can and must still recognize that they form a class of statements entirely different from those of which we come to know empirically. All of them have a property that we agreed to call “tautology” just above. This, combined with the fact that they can be expressed solely in terms of variables and logical constants (where a logical constant is something that remains constant in a statement even when all its constituents change), will give the definition of logic or pure mathematics.
3) Logic- - the doctrine of the connections and sequences of human thinking, the forms of its development, the various relationships of mental forms and their transformations. L. considers questions about the means of existence of thinking, languages of consolidation, reproduction, and translation of thought processes. IN in a broad sense L. is the discernment of connections not only of thinking, but also of being, i.e. L., revealing the “logic of things,” “logic of events,” “connection of times.” In this aspect, L. comes close to ontology. In its substantive aspects, philosophy is associated with the teachings of cognition, its development, functioning, and conservation and is directly included in epistemology. Thus, philosophy is one of the main subdivisions of philosophy and constantly plays a leading role in philosophizing, since the latter always deals with the issue of thinking in one way or another. In the 19th century Philosophy, as a special science, is separated from philosophy and, as such, deals with the formal analysis of thinking and its languages. Questions of the development of thinking, the evolution of its means, its cultural, historical and social conditionality remain within the competence of philosophy. Philosophy itself, in its specific socio-historical and cultural forms, becomes an important branch of philosophical research. Within the framework of this approach, several main stages in the evolution of light and its understanding can be identified. In the ancient world, the development of logical problems was associated with the processes of classification of artificial and natural things, tools of human activity, and acts of human interactions. L. develops generalizing concepts and techniques for operating with them. As part of philosophy, it is an important tool for creating a picture of the world and using it in the practice of society. In the Middle Ages, literature was focused on research into forms of thinking and their relationships; meaningful cognition is considered from the perspective its correspondence to logical forms. The doctrine of stable (or unshakable) structures of human thinking that ensure its correctness turns out to be an important prerequisite for the emerging standards of scientific rationality. When, following natural science, formal philosophy is separated from philosophy, the question of the rationality of human thinking finds itself at the center of philosophical polemics. On the one hand, the insufficiency of formal rationality for the needs of the latest science, for the development of the human personality and expansion of its spiritual horizons. On the other hand, the need to preserve rationality and philosophy in the broadest sense as conditions for the reproduction of culture is confirmed (Baden neo-Kantianism). In the 20th century, philosophical criticism of rationality (usually interpreted as a rigid connection of logical forms) intensifies and is conducted from different positions (existentialism, Marxism, deconstructionism). At the same time, in philosophy there is an increasing tendency to treat literature from a cultural and historical perspective, to study various laws inherent in different cultures and types of human activity. In the light of these approaches, the emphasis in understanding the content of L is changing. If previously this quality was associated mainly with clarifying the objective orientation of thinking, now the focus is on the connection of mental forms that arises in the interaction of human subjects, this interaction is consolidating and reproducing. V. E. Kemerov
4) Logic- - the science of the laws and operations of correct thinking. According to the basic principle of logic, the correctness of reasoning is determined only by its logical form or structure and does not depend on the specific content of the statements included in it. Distinctive feature correct reasoning is that if the premises are true, logical thinking leads to a true conclusion (answer to the question). Incorrect reasoning can lead from true and untrue premises to both true and untrue conclusions (the truth of the conclusion is a matter of chance). Thus, what logic is is clear - these are the rules for using certain mental techniques when processing information. There is formal logic, humanistic logic, women's logic, children's logic, schizophrenic logic, dialectical logic, philosophical logic, etc. But besides logic, there is also thinking itself, which can obey its laws (correct thinking) and not obey (incorrect thinking). illogical thinking). Associative block. From our point of view, logic is a section of the theory of knowledge that studies the relationship and existence of things in the full sense of the last word.
5) Logic- (from Greek – logos): in the broadest sense – the science of thinking, the doctrine of laws, forms and means of reasoning. Most often, this term is identified with the term “formal logic,” the founder of which was Aristotle. The main goal of logical research is to analyze the correctness of reasoning, the formulation of laws and principles, the observance of which is a necessary condition for obtaining true conclusions in the process of inference. Logical processes are studied by representing them in formalized languages. Each of them includes a set of appropriately interpreted expressions (formulas), as well as methods for transforming some expressions into others according to the rules of deduction. Modern logic consists of large number logical systems that describe individual fragments (types) of reasoning. Depending on the basis (criteria) of classification, classical and non-classical logic are currently distinguished. In the modern sense, logic is the science of forms of discourse.
6) Logic- - etymologically goes back to the ancient Greek word “logos”, meaning “word”, “thought”, “concept”, “reasoning”, “law”. This is the science of the laws and forms of human thinking. She studies mental procedures. There is a distinction between traditional logic, which was started by Aristotle, which studies inferences, concepts and operations on them. The use of formalization methods and mathematical methods led to the creation of classical logic (symbolic or mathematical). Non-classical (modal or philosophical) logic, which uses formal methods to analyze meaningful realities. A simplified understanding of logic - the flow of reasoning, the rules of reasoning.
7) Logic- - the science of generally valid forms and means of thought necessary for rational knowledge of any area of reality.
8) Logic - (Greek logos - word, reasoning, concept, mind) - the science of forms, laws and methods of cognitive activity; the ability to think correctly (logically). Since ancient times, an important property of human cognitive thinking has been noticed: if at first some statements are made, then other statements can be recognized, but not any, but only strictly defined ones. Cognitive thinking, therefore, is subject to a certain compulsory force, its results are largely determined and predetermined by previous knowledge. This property was widely used by Socrates in his dialogues. By skillfully posing questions, he directed his interlocutor to the adoption of very specific conclusions. (Characterizing his method, Socrates explained that his manner of conversation is similar to what a midwife does, who does not give birth herself, but takes birth. So he only asks others, contributing to the birth of truth, but he himself has nothing to say.) Therefore, his method Socrates called maieutics - the art of the midwife.) Socrates' student Plato, then Aristotle made the determinism of thinking the subject of special study. Aristotle's results are particularly impressive. His success is due to the fact that he eliminated from the reasoning what can be called their content, retaining only the form. He achieved this by substituting letters (variables) in judgments instead of names with specific contents. For example, in an implicative argument: “If all Bs are Cs and all Aes are Bs, then all Aes are Bs.” Aristotle’s approach demonstrated the fact that the reliability of the results of reasoning with different contents depends not only on the truth of the initial positions (premises), but also on the relationships between them, the method of their connection, i.e. on the form of reasoning. Aristotle formulated the most important principles for the transition from true premises to true conclusions. Subsequently, these principles began to be called the laws of identity, contradiction and excluded middle. He proposed the first theoretical system of forms of reasoning - the so-called. assertoric syllogistic, which deals with propositions of the form “All A are B”, “Some A are B”, “No A is B”, “Some A are not B”. Thus, he laid the foundation for the science of generally valid means and forms of thinking, the laws of rational knowledge. Later this science began to be called L.L. did not limit itself to clarifying cases when the truth of the premises guarantees the truth of the conclusion. This type of reasoning became the subject of one of its branches - deductive L. But Democritus already discusses the problem of inductive inferences, through which the transition from particular statements to general provisions of a probabilistic nature is carried out. Particular interest in induction appears in the 17th and 18th centuries. when experimental sciences began to develop rapidly. The English philosopher F. Bacon made the first attempt at a theoretical understanding of induction, which, as he thought, could serve as the only method of understanding natural phenomena in order to use them for the benefit of people. Deductivism and inductivism were the main directions in the development of literature until the 19th century. Representatives of rationalistic philosophy (Descartes, Spinoza, Malebranche, Leibniz) preferred deduction, while representatives of empirical (sensualistic) philosophy (following F. Bacon - Hobbes, Locke, Condillac, Berkeley, Hume) were inductivists. Wolf, who proposed a comprehensive, in his opinion, system of philosophical knowledge as “the science of all possible objects, as far as they are possible,” tried to reconcile these directions. Being, in general, a rationalist, he nevertheless energetically emphasized the decisive importance of induction and experimental knowledge in certain scientific disciplines (for example, in physics). However, Wolffian ideas about the forms and laws of thinking and methods of cognition, which had developed in Leningrad by the 19th century, were unable to satisfy the needs of rapidly developing science and social practice. Kant and especially Hegel criticized the limitations of the rationalistic-metaphysical method. L. was faced with the task of developing means that would allow a conscious approach to the study of essential relationships. A serious attempt to solve this problem was made by Hegel. His outstanding merit is the introduction of the idea of development and interconnection into literature. This allowed him to lay the foundations of dialectical literature as a theory of the movement of human thought from phenomenon to essence, from relative truth to absolute truth, from abstract knowledge to concrete knowledge. Based on the categories, principles, and laws of dialectical literature, methodological guidelines are developed for studying the content of objects in all their diversity and inconsistency. Currently, literature is a fairly extensive scientific discipline. Its most important and most mature section is formal literature. It received its name from the subject it has been dealing with since ancient times - forms of thoughts and reasoning that ensure the receipt of new truths on the basis of already established ones, and, first of all, the criteria for the correctness and validity of these forms. For a long time, formal literature was known primarily in the form that Aristotle and his commentators gave it. Hence the name corresponding at this stage , - Aristotelian philosophy. The tradition going back to Aristotle also gave rise to another equivalent term - traditional literature. The invariability of the problems and methods of solving them within the framework of Aristotelian literature over many centuries gave reason to Kant, who first used the term “formal literature.”, to believe that two thousand years that have passed since the time of Aristotle, this L. has not taken a single step forward and has an essentially complete character. Kant did not even imagine that just half a century after his death a “second wind” would begin in the development of formal logic. This qualitatively new stage was caused by the fact that the problems posed by the study of the logical foundations of mathematics could not be solved by means of Aristotelian logic. Almost simultaneously The processes of logicalization of mathematics and mathematization of L are underway. When solving logical problems, mathematical methods are actively used, logical calculus is created. Concrete steps are being taken to implement Leibniz's ideas on the use of computational methods in any science. J. Boole develops the first system of algebra L. Thanks to the work of O. de Morgan, W. Jevons, E. Schroeder, P.S. Poretsky, Peirce, Frege, J. Peano, and Russell created the main sections of mathematical mathematics, which became the most important branch of formal mathematics. In the 20th century, especially in the 20s and 30s, in the works of J. Lukasiewicz, E. Post, K Lewis, S. Yaskovsky, D. Webb, L. Brouwer, A. Heyting, A.A. Markova, A.N. Kolmogorov, G. Reichenbach, S.K. Kleene, P. Detouches-Fevrier, G. Birkhoff, and others lay the foundations of non-classical sections of formal linguistics: multi-valued linguistics, modal, probabilistic, intuitionistic, constructivist, and others. The transition to a number of truth values greater than two (“true” ", and "false"), constitutes one of the characteristic features of non-classical, or, as they are often called, non-Chrysippian logic. In the 1930s, the development of formal logic was associated with the solution of many problems of metalogic (Greek meta - after, over), studying principles of construction and general properties of formal systems, for example, problems of consistency, completeness, independence of the system of axioms, solvability, the ability of these systems to express meaningful theories, etc. The foundations of the so-called. "machine thinking" The study of these problems was marked by outstanding discoveries that have important ideological and methodological significance and are associated with the names of Tarski, K. Gödel, A. Church. The most famous is K. Gödel’s theorem on the incompleteness of formalized systems, incl. arithmetic of natural numbers and axiomatic set theory. In accordance with this theorem, in each of these systems there are propositions that within their framework can neither be proven nor disproved. Thus, it was shown that not a single valid scientific theory can be squeezed into the framework of formalism. A. Church proved the theorem according to which there are no algorithms for solving many classes of problems, not to mention an algorithm that allows solving any problem (many outstanding logicians and mathematicians dreamed of inventing such an algorithm). Today, the development of formal logic is proceeding in two main directions: 1) the development of new systems of non-classical logic (the logic of imperatives, evaluations, questions, temporal, inductive logic, the theory of logical implication, etc.), the study of the properties of these systems and the relationships between them, creating them general theory; 2) expansion of the scope of application of formal L. The most important final result obtained in this direction is that formal L. has become not only an instrument of precise thought, but also the “thought” of the first precise instrument - the computer, directly in the role of a partner included by man in the sphere solving the problems facing him. L. (in the sum of all its sections) has become an integral part of human culture. Its achievements are used in a wide variety of areas of human activity. It is widely used in psychology and linguistics, management theory and pedagogy, law and ethics. Its formal sections are the original basis of cybernetics, computational mathematics and technology, and information theory. Without the principles and laws of literature, modern methodology of cognition and communication is unthinkable. The study of L. has always been given great importance. Parmenides already taught Socrates, who was still inexperienced in philosophy: “Your zeal for reasoning, rest assured, is wonderful and divine, but while you are still young, try to practice more in what most consider idle talk (i.e., operating with abstract concepts - V. B.) otherwise the truth will elude you." As we see, already in ancient times it was understood that the discipline, which was later given the name L., plays, first of all, a large methodological role - as a means of finding the truth. V.F. Berkov
9) Logic- - in a broad sense - this is the philosophical science of the laws of correct thinking; in a narrow sense - a sequence of necessities built in the search for truth.
10) Logic - (from the Greek logos - logos) 1) the ability to correctly, i.e. logically, think; 2) the doctrine of identity and its negation (G. Jacobi), the doctrine of consistency and methods of cognition (the science of logic). As "elementary formal logic" it deals with the most general properties inherent in all (existing) concepts. Basic properties of concepts are expressed in logical axioms (see Axiom). First, the doctrine of the concept is considered, then comes the doctrine of judgment and, finally, inference. The doctrines of logical axioms, concepts, judgments and inferences, taken together, form pure logic. Applied logic covers in traditional logic the doctrine of definition, proof, and method. It is often preceded not by scientific-logical, but by theoretical-cognitive, psychological teachings about experience, description and formulation (especially with the help of special language, terminology) and the formation of concepts. Sometimes the doctrine of the system is added to it. Logic (as a science) is only the doctrine of thinking in concepts, but not of knowledge through concepts; it serves to increase the formal accuracy of consciousness and the objectivity of the content of thinking and cognition. The founder of Western European logic (as a science) is Aristotle, the “father of logic.” The word "logic" first appeared among the Stoics; they and the Neoplatonists clarified certain aspects of it, and in the Middle Ages scholasticism developed it in the smallest detail, in subtleties. Humanism expelled scholasticism from logic, but could not renew it. The Reformation adopted the logic of Melanchthon, the Counter-Reformation - the logic of Suarez. Having risen in principle above scholasticism, Johannes Sturm from Strasbourg developed logic; Pierre Ramet became more famous. From the 17th century The influence on logic of the spheres of thought associated with mathematics became noticeable, and in Spinoza’s geometric method it was less than in Leibniz, who used improving natural science methods in logic. From Leibniz and mathematics, as well as from neo-scholasticism, came the logic of the Wolf school. Kant's "transcendental logic" is in reality a critical theory of knowledge, a logic of German. idealism (especially Hegel's logic) - speculative metaphysics. Schopenhauer, Nietzsche, Bergson and proponents of the philosophy of life rejected traditional logic. Currently, logic has split into many directions: 1) metaphysical logic (Hegelianism); 2) psychological logic (T. Lipps, partly W. Wundt); 3) epistemological, or transcendental, logic (neo-Kantianism); 4) semantic logic (Aristotle, Kulpe, modern nominalism); 5) subject logic (Remke, Meinong, Drish); 6) neo-scholastic logic; 7) phenomenological logic; 8) logic as methodology (neo-Kantianism) and logistics, which is at the center of debates about logic.
11) Logic- - see Dialectical logic. Mathematical logic, Formal logic.
Logics
In the book: 1) the universal boundary of the givenness of things in the world, which itself remains invisible; 2) a technique for indirectly identifying this boundary.
Activity can provide only one half of wisdom; the other half depends on perceptive inactivity. Ultimately, the debate between those who base logic on "truth" and those who base it on "research" stems from differences in values and at a certain point becomes meaningless. In logic it is a waste of time to consider conclusions concerning particular cases; we always deal with completely general and purely formal implications, leaving for other sciences the study of in which cases the assumptions are confirmed and in which they are not. Although we can no longer be content with defining logical statements as following from the law of contradiction, we can and must still recognize that they form a class of statements entirely different from those of which we come to know empirically. All of them have a property that we agreed to call “tautology” just above. This, combined with the fact that they can be expressed solely in terms of variables and logical constants (where a logical constant is something that remains constant in a statement even when all its constituents change), will give the definition of logic or pure mathematics.
The doctrine of the connections and sequences of human thinking, the forms of its development, the various relationships of mental forms and their transformations. L. considers questions about the means of existence of thinking, languages of consolidation, reproduction, and translation of thought processes. In a broad sense, philosophy is an examination of the connections not only of thinking, but also of being, that is, literature that reveals the “logic of things,” the “logic of events,” and the “connection of times.” In this aspect, L. comes close to ontology. In its substantive aspects, philosophy is associated with the teachings of cognition, its development, functioning, and conservation and is directly included in epistemology. Thus, philosophy is one of the main subdivisions of philosophy and constantly plays a leading role in philosophizing, since the latter always deals with the issue of thinking in one way or another. In the 19th century Philosophy, as a special science, is separated from philosophy and, as such, deals with the formal analysis of thinking and its languages. Questions of the development of thinking, the evolution of its means, its cultural, historical and social conditionality remain within the competence of philosophy. Philosophy itself, in its specific socio-historical and cultural forms, becomes an important branch of philosophical research. Within the framework of this approach, several main stages in the evolution of light and its understanding can be identified. In the ancient world, the development of logical problems was associated with the processes of classification of artificial and natural things, tools of human activity, and acts of human interactions. L. develops generalizing concepts and techniques for operating with them. As part of philosophy, it is an important tool for creating a picture of the world and using it in the practice of society. In the Middle Ages, literature was focused on research into forms of thinking and their relationships; meaningful cognition is considered from the perspective its correspondence to logical forms. The doctrine of stable (or unshakable) structures of human thinking that ensure its correctness turns out to be an important prerequisite for the emerging standards of scientific rationality. When, following natural science, formal philosophy is separated from philosophy, the question of the rationality of human thinking finds itself at the center of philosophical polemics. On the one hand, the insufficiency of formal rationality for the needs of modern science, for the development of the human personality and the expansion of its spiritual horizons is revealed. On the other hand, the need to preserve rationality and philosophy in the broadest sense as conditions for the reproduction of culture is confirmed (Baden neo-Kantianism). In the 20th century, philosophical criticism of rationality (usually interpreted as a rigid connection of logical forms) intensifies and is conducted from different positions (existentialism, Marxism, deconstructionism). At the same time, in philosophy there is an increasing tendency to treat literature from a cultural and historical perspective, to study various laws inherent in different cultures and types of human activity. In the light of these approaches, the emphasis in understanding the content of L is changing. If previously this quality was associated mainly with clarifying the objective orientation of thinking, now the focus is on the connection of mental forms that arises in the interaction of human subjects, this interaction is consolidating and reproducing. V. E. Kemerov
The science of the laws and operations of correct thinking. According to the basic principle of logic, the correctness of reasoning is determined only by its logical form or structure and does not depend on the specific content of the statements included in it. A distinctive feature of correct reasoning is that if the premises are true, logical thinking leads to a true conclusion (the answer to the question). Incorrect reasoning can lead from true and untrue premises to both true and untrue conclusions (the truth of the conclusion is a matter of chance). Thus, what logic is is clear - these are the rules for using certain mental techniques when processing information. There is formal logic, humanistic logic, women's logic, children's logic, schizophrenic logic, dialectical logic, philosophical logic, etc. But besides logic, there is also thinking itself, which can obey its laws (correct thinking) and not obey (incorrect thinking). illogical thinking). Associative block. From our point of view, logic is a section of the theory of knowledge that studies the relationship and existence of things in the full sense of the last word.
(from Greek - logos): in the broadest sense - the science of thinking, the doctrine of laws, forms and means of reasoning. Most often, this term is identified with the term “formal logic,” the founder of which was Aristotle. The main goal of logical research is to analyze the correctness of reasoning, the formulation of laws and principles, the observance of which is a necessary condition for obtaining true conclusions in the process of inference. Logical processes are studied by representing them in formalized languages. Each of them includes a set of appropriately interpreted expressions (formulas), as well as methods for transforming some expressions into others according to the rules of deduction. Modern logic is composed of a large number of logical systems that describe individual fragments (types) of reasoning. Depending on the basis (criteria) of classification, classical and non-classical logic are currently distinguished. In the modern sense, logic is the science of forms of discourse.
Etymologically, it goes back to the ancient Greek word “logos”, meaning “word”, “thought”, “concept”, “reasoning”, “law”. This is the science of the laws and forms of human thinking. She studies mental procedures. There is a distinction between traditional logic, which was started by Aristotle, which studies inferences, concepts and operations on them. The use of formalization methods and mathematical methods led to the creation of classical logic (symbolic or mathematical). Non-classical (modal or philosophical) logic, which uses formal methods to analyze meaningful realities. A simplified understanding of logic - the flow of reasoning, the rules of reasoning.
The science of generally valid forms and means of thought necessary for rational knowledge of any area of reality.
(Greek logos - word, reasoning, concept, mind) - the science of forms, laws and methods of cognitive activity; the ability to think correctly (logically). Since ancient times, an important property of human cognitive thinking has been noticed: if at first some statements are made, then other statements can be recognized, but not any, but only strictly defined ones. Cognitive thinking, therefore, is subject to a certain compulsory force, its results are largely determined and predetermined by previous knowledge. This property was widely used by Socrates in his dialogues. By skillfully posing questions, he directed his interlocutor to the adoption of very specific conclusions. (Characterizing his method, Socrates explained that his manner of conversation is similar to what a midwife does, who does not give birth herself, but takes birth. So he only asks others, contributing to the birth of truth, but he himself has nothing to say.) Therefore, his method Socrates called maieutics - the art of the midwife.) Socrates' student Plato, then Aristotle made the determinism of thinking the subject of special study. Aristotle's results are particularly impressive. His success is due to the fact that he eliminated from the reasoning what can be called their content, retaining only the form. He achieved this by substituting letters (variables) in judgments instead of names with specific contents. For example, in an implicative argument: “If all Bs are Cs and all Aes are Bs, then all Aes are Bs.” Aristotle’s approach demonstrated the fact that the reliability of the results of reasoning with different contents depends not only on the truth of the initial positions (premises), but also on the relationships between them, the method of their connection, i.e. on the form of reasoning. Aristotle formulated the most important principles for the transition from true premises to true conclusions. Subsequently, these principles began to be called the laws of identity, contradiction and excluded middle. He proposed the first theoretical system of forms of reasoning - the so-called. assertoric syllogistic, which deals with propositions of the form “All A are B”, “Some A are B”, “No A is B”, “Some A are not B”. Thus, he laid the foundation for the science of generally valid means and forms of thinking, the laws of rational knowledge. Later this science began to be called L.L. did not limit itself to clarifying cases when the truth of the premises guarantees the truth of the conclusion. This type of reasoning became the subject of one of its branches - deductive L. But Democritus already discusses the problem of inductive inferences, through which the transition from particular statements to general provisions of a probabilistic nature is carried out. Particular interest in induction appears in the 17th and 18th centuries. when experimental sciences began to develop rapidly. The English philosopher F. Bacon made the first attempt at a theoretical understanding of induction, which, as he thought, could serve as the only method of understanding natural phenomena in order to use them for the benefit of people. Deductivism and inductivism were the main directions in the development of literature until the 19th century. Representatives of rationalistic philosophy (Descartes, Spinoza, Malebranche, Leibniz) preferred deduction, while representatives of empirical (sensualistic) philosophy (following F. Bacon - Hobbes, Locke, Condillac, Berkeley, Hume) were inductivists. Wolf, who proposed a comprehensive, in his opinion, system of philosophical knowledge as “the science of all possible objects, as far as they are possible,” tried to reconcile these directions. Being, in general, a rationalist, he nevertheless energetically emphasized the decisive importance of induction and experimental knowledge in certain scientific disciplines (for example, in physics). However, Wolffian ideas about the forms and laws of thinking and methods of cognition, which had developed in Leningrad by the 19th century, were unable to satisfy the needs of rapidly developing science and social practice. Kant and especially Hegel criticized the limitations of the rationalistic-metaphysical method. L. was faced with the task of developing means that would allow a conscious approach to the study of essential relationships. A serious attempt to solve this problem was made by Hegel. His outstanding merit is the introduction of the idea of development and interconnection into literature. This allowed him to lay the foundations of dialectical literature as a theory of the movement of human thought from phenomenon to essence, from relative truth to absolute truth, from abstract knowledge to concrete knowledge. Based on the categories, principles, and laws of dialectical literature, methodological guidelines are developed for studying the content of objects in all their diversity and inconsistency. Currently, literature is a fairly extensive scientific discipline. Its most important and most mature section is formal literature. It received its name from the subject it has been dealing with since ancient times - forms of thoughts and reasoning that ensure the receipt of new truths on the basis of already established ones, and, first of all, the criteria for the correctness and validity of these forms. For a long time, formal literature was known primarily in the form that Aristotle and his commentators gave it. Hence the name corresponding to this stage is Aristotelian L. The tradition going back to Aristotle also gave rise to another equivalent term - traditional philosophy. The invariability of the problem and methods of resolving it within the framework of Aristotelian philosophy over many centuries gave the basis to Kant, who first used the term “formal philosophy,” to believe that over the two thousand years that have passed Since the time of Aristotle, this L. has not taken a single step forward and has an essentially complete character. Kant did not even imagine that just half a century after his death a “second wind” would begin in the development of formal logic. This qualitatively new stage was caused by the fact that the problems posed by the study of the logical foundations of mathematics could not be solved by means of Aristotelian logic. Almost simultaneously The processes of logicalization of mathematics and mathematization of L are underway. When solving logical problems, mathematical methods are actively used, logical calculus is created. Concrete steps are being taken to implement Leibniz's ideas on the use of computational methods in any science. J. Boole develops the first system of algebra L. Thanks to the work of O. de Morgan, W. Jevons, E. Schroeder, P.S. Poretsky, Peirce, Frege, J. Peano, and Russell created the main sections of mathematical mathematics, which became the most important branch of formal mathematics. In the 20th century, especially in the 20s and 30s, in the works of J. Lukasiewicz, E. Post, K Lewis, S. Yaskovsky, D. Webb, L. Brouwer, A. Heyting, A.A. Markova, A.N. Kolmogorov, G. Reichenbach, S.K. Kleene, P. Detouches-Fevrier, G. Birkhoff, and others lay the foundations of non-classical sections of formal linguistics: multi-valued linguistics, modal, probabilistic, intuitionistic, constructivist, and others. The transition to a number of truth values greater than two (“true” ", and "false"), constitutes one of the characteristic features of non-classical, or, as they are often called, non-Chrysippian logic. In the 1930s, the development of formal logic was associated with the solution of many problems of metalogic (Greek meta - after, over), studying principles of construction and general properties of formal systems, for example, problems of consistency, completeness, independence of the system of axioms, solvability, the ability of these systems to express meaningful theories, etc. The foundations of the so-called. "machine thinking" The study of these problems was marked by outstanding discoveries that have important ideological and methodological significance and are associated with the names of Tarski, K. Gödel, A. Church. The most famous is K. Gödel’s theorem on the incompleteness of formalized systems, incl. arithmetic of natural numbers and axiomatic set theory. In accordance with this theorem, in each of these systems there are propositions that within their framework can neither be proven nor disproved. Thus, it was shown that not a single valid scientific theory can be squeezed into the framework of formalism. A. Church proved the theorem according to which there are no algorithms for solving many classes of problems, not to mention an algorithm that allows solving any problem (many outstanding logicians and mathematicians dreamed of inventing such an algorithm). Today, the development of formal logic is proceeding in two main directions: 1) the development of new systems of non-classical logic (the logic of imperatives, evaluations, questions, temporal, inductive logic, the theory of logical implication, etc.), the study of the properties of these systems and the relationships between them, the creation of their general theory; 2) expansion of the scope of application of formal L. The most important final result obtained in this direction is that formal L. has become not only an instrument of precise thought, but also the “thought” of the first precise instrument - the computer, directly in the role of a partner included by man in the sphere solving the problems facing him. L. (in the sum of all its sections) has become an integral part of human culture. Its achievements are used in a wide variety of areas of human activity. It is widely used in psychology and linguistics, management theory and pedagogy, law and ethics. Its formal sections are the original basis of cybernetics, computational mathematics and technology, and information theory. Without the principles and laws of literature, modern methodology of cognition and communication is unthinkable. The study of L. has always been given great importance. Parmenides already taught Socrates, who was still inexperienced in philosophy: “Your zeal for reasoning, rest assured, is wonderful and divine, but while you are still young, try to practice more in what most consider idle talk (i.e., operating with abstract concepts - V. B.) otherwise the truth will elude you." As we see, already in ancient times it was understood that the discipline, which was later given the name L., plays, first of all, a large methodological role - as a means of finding the truth. V.F. Berkov
In a broad sense, it is a philosophical science about the laws of correct thinking; in a narrow sense - a sequence of necessities built in the search for truth.
(from Greek logos - logos) 1) the ability to correctly, i.e. logically, think; 2) the doctrine of identity and its negation (G. Jacobi), the doctrine of consistency and methods of cognition (the science of logic). As "elementary formal logic" it deals with the most general properties inherent in all (existing) concepts. Basic properties of concepts are expressed in logical axioms (see Axiom). First, the doctrine of the concept is considered, then comes the doctrine of judgment and, finally, inference. The doctrines of logical axioms, concepts, judgments and inferences, taken together, form pure logic. Applied logic covers in traditional logic the doctrine of definition, proof, and method. It is often preceded not by scientific-logical, but by theoretical-cognitive, psychological teachings about experience, description and formulation (especially with the help of special language, terminology) and the formation of concepts. Sometimes the doctrine of the system is added to it. Logic (as a science) is only the doctrine of thinking in concepts, but not of knowledge through concepts; it serves to increase the formal accuracy of consciousness and the objectivity of the content of thinking and cognition. The founder of Western European logic (as a science) is Aristotle, the “father of logic.” The word "logic" first appeared among the Stoics; they and the Neoplatonists clarified certain aspects of it, and in the Middle Ages scholasticism developed it in the smallest detail, in subtleties. Humanism expelled scholasticism from logic, but could not renew it. The Reformation adopted the logic of Melanchthon, the Counter-Reformation - the logic of Suarez. Having risen in principle above scholasticism, Johannes Sturm from Strasbourg developed logic; Pierre Ramet became more famous. From the 17th century The influence on logic of the spheres of thought associated with mathematics became noticeable, and in Spinoza’s geometric method it was less than in Leibniz, who used improving natural science methods in logic. From Leibniz and mathematics, as well as from neo-scholasticism, came the logic of the Wolf school. Kant's "transcendental logic" is in reality a critical theory of knowledge, a logic of German. idealism (especially Hegel's logic) - speculative metaphysics. Schopenhauer, Nietzsche, Bergson and proponents of the philosophy of life rejected traditional logic. Currently, logic has split into many directions: 1) metaphysical logic (Hegelianism); 2) psychological logic (T. Lipps, partly W. Wundt); 3) epistemological, or transcendental, logic (neo-Kantianism); 4) semantic logic (Aristotle, Kulpe, modern nominalism); 5) subject logic (Remke, Meinong, Drish); 6) neo-scholastic logic; 7) phenomenological logic; 8) logic as methodology (neo-Kantianism) and logistics, which is at the center of debates about logic.
The asymmetrical opposite of the absolute, characterized by negative extension, anti-substantiality, self-destructive...
