Logical thinking is the development of logic. Control work specifics of logic as a science Place in the system of sciences of traditional logic
Features of modern logic
The immediate result of the revolution that took place in logic at the end of the 19th and beginning of the 20th centuries was the emergence of a logical theory, which over time received the name "classical logic". Its origins are the Irish logician D. Buhl, the American philosopher and logician C. Pierce, and the German logician G. Frege. In their work, the idea of transferring to logic those methods that are usually used in mathematics was realized. Classical logic still remains the core of modern logic, retaining both theoretical and practical significance. Thus, classical logic continues the traditions of the Aristotelian direction in the development of logic, while using the modern mathematical and categorical apparatus.
However, at the beginning of the XX century. criticism of classical logic began. As a result, many new directions arose, which were called non-classical logic.
Unlike classical logic, non-classical logic has not been formed as a single whole, but is a heterogeneous direction.
intuitionistic logic
In 1908, the Dutch mathematician and logician L. Brouwer questioned the unlimited applicability in mathematical reasoning of the classical laws of the excluded middle (which states that either the statement itself or its negation is true), double negation, and indirect proof. As a result of this analysis in 1930, intuitionistic logic arose, which did not contain these laws. The law of the excluded middle, Brouwer believed, arose in reasoning about a finite set of objects. Then it was extended to infinite sets. When a set is finite, we can decide whether all the objects in it have some property by checking all the objects in the set one by one. For infinite sets, such a check is impossible.
In the words of the German mathematician G. Weil, the proof of existence, based on the law of the excluded middle, informs the world about the existence of a treasure, while not indicating the location and not giving the opportunity to use it.
Highlighting mathematical intuition, intuitionists did not attach much importance to the systematization of logical rules. It was only in 1930 that Brouwer's student A. Rating published a work expounding a special intuitionistic logic.
Later, ideas concerning the limited applicability of the law of the excluded middle and methods of mathematical proof close to it were developed by Russian scientists A. N. Kolmogorov, V. A. Glivenko, A. A. Markov and others.
Multivalued logic
In the 20s. a new direction began to take shape - multi-valued logic. A feature of classical logic is the principle that every proposition is either true or false. This is the so-called ambiguity principle. It is opposed by many-valued systems. In them, along with true and false judgments, indefinite judgments are allowed, taking into account which changes the whole picture of reasoning.
The principle of ambiguity was already known to Aristotle, who, however, did not consider it universal and did not extend its action to statements about the future. It seemed to Aristotle that statements about future random events, the occurrence of which depends on a person, are neither true nor false. They do not obey the principle of ambiguity. The past and the present are unambiguously determined and are not subject to change. The future is, to a certain extent, free for change and choice.
Aristotle's approach has already caused fierce controversy in antiquity. He was highly appreciated by Epicurus, who allowed the existence of random events. Another ancient Greek logician Chrysippus, who categorically denied the accidental, did not agree with Aristotle. He considered the principle of ambiguity to be one of the main provisions not only of all logic, but also of philosophy.
In more recent times, the position that every proposition is either true or false has been disputed by many logicians and for many reasons. In particular, it was pointed out that this principle is inapplicable to statements about unstable, transitional states, about non-existent objects, about objects that are inaccessible to observation.
But only in modern logic it was possible to realize doubts about the universality of the principle of ambiguity in the form of logical systems. The first many-valued logics were built independently by the Polish logician J. Lukasiewicz in 1920 and the American logician E. Post in 1921.
Lukasiewicz proposed a three-valued logic based on the assumption that statements are true, false and indefinite. The latter included statements like: "Students will go on vacation in the summer." The event described by this statement is not currently defined in any way - either positively or negatively. Hence, the statement is neither true nor false, it is only possible.
All the laws of Lukasiewicz's three-valued logic also turned out to be the laws of classical logic, but the converse statement made no sense. A number of classical laws were absent in three-valued logic. Among them were the law of contradiction, the law of the excluded middle, the law of circumstantial evidence, and a number of others.
Unlike Lukasiewicz, E. Post approached the construction of many-valued logic in a purely formal way. Let's say 1 means true and 0 means false. It is natural to assume that numbers between one and zero denote degrees of truth.
At the same time, in order for the construction of a logical system to cease to be a purely technical exercise, and the system itself to cease to be a purely formal construction, it is necessary to give the symbols of this system a certain logical meaning and meaningful interpretation. The question of such an interpretation is the most difficult and controversial problem of many-valued logics. As soon as something intermediate is allowed between truth and falsehood, the question arises: what do statements that are neither true nor false mean? In addition, the introduction of intermediate degrees of truth changes the usual meaning of the very concepts of truth and falsehood.
There have been many attempts to meaningfully substantiate multivalued logical systems, but there is still no satisfactory explanation.
Relevant logic
Classical logic has been criticized for not giving a correct description of logical consequence. The main task of logic is the systematization of rules that allow deriving new ones from accepted statements. Logical consequence is the relationship that exists between statements and the conclusions that are validly deduced from them. The task of logic is to clarify the intuitive idea of following and to formulate on this basis a uniquely defined concept of following. Logical following should lead from true positions only to true ones. Classical logic satisfies these requirements, but many of its provisions do not agree well with our usual ideas. In particular, classical logic says that the following statements follow from the contradictory judgments “Student Ivanov is an excellent student” and “Student Ivanov is not an excellent student”: “Students do not want to study.” But there is no substantive connection between the original statement and these statements allegedly arising from it. There is a departure from the usual notion of following here. The consequence that is derived must be somehow related to what it is derived from. Classical logic neglects this obvious circumstance.
As far back as 1912, the American logician C. I. Lewis drew attention to these so-called "paradoxes of implication". He developed a non-classical theory of logical consequence, which was based on the concept of strict implication. This concept was most fully developed in the relevant logic developed by the American logicians A. R. Anderson and N. D. Belnap.
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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.
LOGIC AS A SCIENCE
1. The subject of logic
2. The emergence and development of logic
3. The language of logic
4. Forms and laws of thinking
1. Subject of logic
Key words: logic, thinking, sensory knowledge, abstract thinking.
Logic (from the Greek: logos - word, concept, mind) 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 around him and himself. Thinking is a process of indirect reflection of reality in the form of ideal images.
Forms and methods of thinking that contribute to the knowledge of the truth. A person acquires knowledge about the phenomena of the world in the process of active purposeful cognition: the subject is 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 the correct conclusions, when the truth of the original knowledge implies the truth of the conclusions.
We know that the first level is sensory cognition. It is carried out on the basis of the sense organs, their comprehension and synthesis. Let us recall the main forms of sensory cognition:
1) feeling;
2) perception;
3) presentation.
This level of cognition has a number of important techniques, among which are the analysis and systematization of sensations, building impressions into a holistic image, memorization and recollection of previously acquired knowledge, imagination, etc. Sensory cognition provides knowledge about external, individual properties and qualities of phenomena. Man, on the other hand, strives to cognize the deep properties and essences of things and phenomena, the laws of the existence of the world and society. Therefore, he resorts to the study of the problems of interest to him at the abstract-theoretical level. At this level, such forms of abstract knowledge are formed 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, highlighting the essential, deriving 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 forms knowledge obtained directly from experience in the form of ideal images based on sensations, experiences, impressions, etc. Abstract thinking marks the transition from studying individual aspects of objects to comprehending 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. Distracting from a single object and a temporary state, thinking is able to single out in them the general and the recurring, the essential and the necessary.
Abstract thinking is inextricably linked with language. Language is the main means of fixing thought. In the linguistic form, not only meaningful meanings are stated, but also logical ones. With the help of language, a person formulates, expresses and transmits thoughts, fixes knowledge.
It is important to understand that our thinking indirectly reflects reality: through a series of interconnected knowledge, by logical consequences, it is possible to come to new knowledge without directly contacting the objective-sense world.
The significance of logic in cognition follows from the possibility of deriving reliable knowledge not only in a formal-logical way, but also in a dialectical way.
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 lies in the development of research programs and technologies suitable for obtaining objective knowledge. This contributes to arming a person with the main means, methods and methods of scientific and theoretical knowledge.
The second main function of logic is analytical-critical, realizing which it acts as a means of detecting errors in reasoning and controlling the correctness of the construction of thought.
Logic is also able to perform epistemological tasks. Without dwelling on 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 cognizing 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 |
The term "logic" comes from the Greek. Logos- “thought”, “word”, “reason”, “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”, “logic of things”, “logic of history”, etc. Secondly, to designate regularities in the development of thought, for example, “logic of reasoning”, “the logic of thinking”, etc. Thirdly, the science of the laws of thinking is called logic.
Thinking is studied by many sciences: psychology, cybernetics, physiology, etc. A feature of logic is that its subject is the forms and methods of correct thinking. Logic as a science includes such sections as formal logic, dialectical, symbolic, modal, etc.
So, logics – it is the science of the ways and forms of correct thinking. The logical form of a particular thought is the structure of this thought, that is, the way in which its constituent parts are connected. Let us explain the meaning of the concept “form of thinking” using an example. Take two sentences: "All men are mortal" and "All rivers flow into the sea." One of them is correct, the other is not. But in form they are the same. Each of them asserts something about a different subject. If we designate the thing that is said by the letter S, and that which is said by the letter P, we get the form of thought: all S is P; it can contain different content. In formal logic, the main forms of thinking are considered: the concept, judgment and inference, as well as the laws of their relationship, observing which one can obtain correct conclusions, provided that the initial positions are true. The logical form, or the form of thinking, is a way of connecting the elements of thought, its structure, thanks to which the content exists and reflects reality.
In the real process of thinking, the content and form of thought exist in an inseparable unity. There is no "pure", devoid of form content, there are no "pure", meaningless logical forms. However, for the purposes of a special analysis, we have the right to abstract from the specific content of thought, making its form the subject of study.
Knowledge of logic increases the culture of thinking, contributes to the clarity, consistency and evidence of reasoning, enhances the effectiveness and persuasiveness of speech. It is especially important to know the basics of logic in the process of mastering new knowledge, it helps to notice logical errors in oral speech and in the written works of other people, to find shorter and more correct ways to refute these errors, and not to make them yourself.
Logic contributes to the formation of self-consciousness, the intellectual development of the individual, helps to form her scientific worldview.
Knowledge of logic is urgently needed for representatives of the media and medical workers, whose activities can affect the fate of people.
A court decision can be correct if not only its legal grounds are correct, but also the reasoning and logic are correct. Logic is of great importance for solving the whole range of legal problems, regulating labor, property and other relations, social and legal protection of citizens, etc.
№2 basic forms of knowledge. Sensual knowledge and abstract thinking and their relationship. Features of abstract thinking
Classification of methods of argumentation 2. The task of argumentation is to develop a belief or opinion in the truth of a statement. Belief and opinion can, of course, be developed not only on the basis of argumentation or observation and practical activity, but also by suggestion based on faith, etc. The statement that is justified is called the argumentation thesis.
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Introduction. The specificity of logic as a science
1. Argumentation and its main forms
1.1 Absolute and comparative justification
1.2. Classification of methods of argumentation
2. Practical part
2.1. Example #1
2.2. Example #2
2.3. Example #3
2.4. Example #4
2.5. Example #5
Conclusion
Bibliography
Introduction. The specifics of logic as a science.
Logic got its name from the ancient Greek word "logos", meaning, on the one hand, the word, speech, and on the other hand, thought, meaning, mind.
Logic, one of the oldest sciences, arose in the problematic field of philosophy, more than 2300 years ago, and in the writings of the ancient Greek philosopher Aristotle, for the first time showed how thinking should be done in order for truth to be achieved.
Arising within the framework of ancient philosophy as a single body of knowledge about the surrounding world that was not yet divided into separate sciences, it was already then considered as a peculiar, namely rational, or speculative, form of philosophy, in contrast to natural philosophy (philosophy of nature) and ethics (social philosophy). philosophy).
In its subsequent development, logic became an increasingly complex, multifaceted phenomenon of the spiritual life of mankind. Therefore, it is natural that in different historical periods it received a different assessment from different thinkers. Some spoke of it as a kind of technical means - a practical "instrument of thought" ("Organon"). Others saw in it a special "art" - the art of thinking and reasoning. Still others found in it a kind of "regulator" - a set or set of rules, regulations and norms of mental activity ("Canon"). There were even attempts to present it as a kind of "medicine" - a means of improving the mind.
There is no doubt that there is some truth in all such assessments. But only a share. The main thing that characterizes logic, especially at the present time, is that it is a science - and, moreover, a very developed and important one. And like any science, it is capable of performing various functions in society, and therefore, acquiring various “faces”. What is the place of logic in the system of sciences?
Today there is a great variety of different branches of scientific knowledge. Depending on the object of study, they are, as you know, divided primarily into natural sciences - natural sciences (astronomy, physics, chemistry, biology, etc.) and social sciences - social sciences (history, sociology, legal sciences).
Compared with them, the originality of logic lies in the fact that its object is thinking. This is the science of thinking. But if we give logic only such a definition and put an end to it, then we will make a serious mistake. The fact is that thinking itself, being the most complex phenomenon, is the object of study not only of logic, but also of a number of other sciences - philosophy, psychology, physiology of higher nervous activity of a person, cybernetics, linguistics ...
What is the specificity of logic in comparison with these sciences that study thinking? What, in other words, is its own subject of study?
Philosophy, the most important section of which is the theory of knowledge, explores thinking as a whole. It solves a fundamental philosophical question related to the attitude of a person, and therefore his thinking, to the world around him: how does our thinking relate to the world itself, can we have a correct mental picture of it in our knowledge?
Psychology studies thinking as one of the mental processes along with emotions, will, etc. It reveals interaction with them; thinking in the course of practical activity and scientific knowledge, analyzes the motives of human mental activity, reveals the peculiarities of the thinking of children, adults, mentally normal people and people with various mental disorders.
The physiology of the higher nervous activity of a person reveals the material, namely the physiological processes occurring in the cortex of the cerebral hemispheres of the human brain, 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, consequently, in a person’s thinking, which is primarily associated 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 peculiarity 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, from the point of view of its role and meaning as a means of knowing reality and at the same time the same time in terms of its constituent elements and the relationships between them. This is its own, specific subject of logic.
Therefore, logic is the science of the forms and laws of correct thinking, leading to truth, or the science of the laws that correct thinking obeys. Right thinking is thinking by which truth is attained.
1. Argumentation and its main forms.
Argumentation is one of the ways to justify statements (judgments, hypotheses, concepts, etc.). Statements can be substantiated by direct reference to reality (through observation, experiment and other types of practical activity), as well as with the help of already known provisions (arguments) and means of logic. In the second case, justification is also carried out by referring to reality, but directly, but indirectly.
Argumentation is a full or partial substantiation of a statement using other statements. It is assumed that in good (correct) arguments, other statements are fully or at least partially substantiated and the justified position follows logically from them or, at least, they confirm it.
The task of argumentation is to develop a belief or opinion in the truth of a statement. Belief is complete confidence in the truth, opinion is also certainty, but not complete. Conviction and opinion can, of course, be developed not only on the basis of argumentation or observation and practical activity, but also by suggestion, on the basis of faith, etc.
Argumentation is the process of forming a belief or opinion about the truth of a statement (judgment, hypothesis, concept, etc.) using other statements.
The statement that is justified is called the argumentation thesis. The statements used to substantiate the thesis are called arguments, or grounds. The logical structure of the argument, i.e. the method of logical substantiation of the thesis by means of arguments is called the form of argumentation.
Proof is a special case of argumentation.
Proof is an argumentation in which the arguments are statements whose truth is established, and the form is demonstrative reasoning (reasoning that provides a true conclusion with true premises). Argumentation can be divided into evidence and non-evidence.
There are three types of unproven (correct) arguments:
1) the arguments are not reliable, but only plausible statements, and the form is demonstrative reasoning. The thesis in such an argument is only plausible because of the unreliability of the arguments.
2) argumentation, in which the arguments are reliable statements, and the form is non-demonstrative reasoning. In these arguments, the thesis is only a plausible statement due to the non-demonstrative form.
3) In non-proven arguments of the third type, the arguments are fully justified statements, and the form is non-demonstrative reasoning.
On another basis, two types of (correct) arguments can be distinguished - direct and indirect types of argumentation. In direct argumentation, reasoning proceeds from arguments to a thesis. With indirect argumentation, it is required to substantiate a certain statement (thesis). Indirect arguments can be evidentiary and non-proven.
1.1. Absolute and comparative justification.
The structure of absolute and comparative justification. In the most general sense, to substantiate a statement means to give those convincing or sufficient reasons by virtue of which it should be accepted.
Absolute justification is the presentation of convincing arguments, by virtue of which the justified provision should be accepted. This justification refers to a single claim and is a set of arguments in support of it.
Comparative reasoning is a system of convincing arguments in support of the fact that it is better to accept the justified position than another position that is opposed to it. It concerns a pair of related statements and is a system of arguments in support of one of the statements being accepted and not the other.
The basis of justification is the totality of arguments given in support of the justified position.
Argumentation techniques can be, and almost always are, richer and sharper than justification techniques. But all methods of argumentation that go beyond the scope of methods of substantiation are obviously less universal and, in most audiences, less convincing than methods of substantiation.
1.2. Classification of methods of argumentation.
Universal and contextual reasoning.
As the basis for the classification, it is proposed to use the nature of the audience, which is subject to the impact of the argument. Then all methods of argumentation can be divided into universal and contextual.
Universal reasoning applies to any audience. The universal methods of argumentation include direct (empirical) confirmation, indirect empirical confirmation (in particular, confirmation of consequences), various methods of theoretical argumentation: deductive justification, systemic argumentation, methodological argumentation, etc.
Contextual reasoning is effective only in a certain audience. Contextual methods of argumentation cover arguments to tradition and authority, to intuition and faith, to common sense and taste, etc.
The boundary between universal and contextual reasoning is relative. Methods of argumentation, at first glance, universally applicable, may be ineffective in a particular audience. Conversely, some contextual arguments, like arguments about tradition or intuition, can be persuasive in just about any audience.
Universal reasoning is sometimes characterized as "rational" and contextual reasoning as "irrational" or even "irrational". Such a distinction is not, as will be clear from what follows, justified. It sharply narrows the scope of the “rational”, excluding from it most of the humanitarian and practical reasoning, which is unthinkable without the use of the “classics” (authorities), the continuation of tradition, an appeal to common sense, taste, etc.
Empirical and theoretical reasoning. All the diverse methods of universal argumentation can be divided into empirical and theoretical.
Empirical argumentation is an argumentation, an integral element of which is a reference to experience, to empirical data.
Theoretical argumentation is an argumentation based on reasoning and not using direct references to experience.
The difference between empirical and theoretical reasoning is relative, just as the very boundary between empirical and theoretical knowledge is relative. It is not uncommon for cases when references to experience and theoretical reasoning are combined in the same process of argumentation.
General classification. Of the various methods of theoretical argumentation, the following are of particular importance:
* deductive reasoning (derivation of a substantiated statement from other previously accepted statements),
*systemic argumentation (substantiation of the statement by including it in a well-tested system of statements, or theory),
* fundamental testability and fundamental refutation (demonstration of the fundamental possibility of empirical confirmation and empirical refutation of the assertion being substantiated),
*compatibility condition (showing that the justified position is in good agreement with the laws, principles and theories related to the field of phenomena under study),
* methodological argumentation (substantiation of the statement by referring to the reliable method by which it was obtained).
All the mentioned methods of universal (empirical and theoretical) and contextual argumentation form the basis of all methods of argumentation, but, of course, they do not exhaust the many possible methods of persuasion.
Direct confirmation is the direct observation of those phenomena that are mentioned in the substantiated statement.
With indirect confirmation, we are talking about confirming the logical consequences of the assertion being justified, and not about direct confirmation of the assertion itself.
deduction and induction. In science, and not only in it, direct observation of what is said in a testable statement is rare. Typically, empirical evidence is inductive evidence, and empirical reasoning takes the form of inductive reasoning.
Depending on whether there is a connection of logical consequence between its premises and conclusion in the inference, two types of inferences are distinguished: deductive and inductive.
In deductive reasoning, the connection between the premises of the conclusion is based on the law of logic, whereby the conclusion logically follows (logically follows) from the premises. Such a conclusion always leads from the true premises to the true conclusion.
In inductive reasoning, the premises and the conclusion are not connected by a law of logic, and the conclusion does not follow logically from the premises. The validity of the premises does not guarantee the validity of the inductively inferred conclusion. It follows from the premises not necessarily, but only with some probability. The concept of deduction (deductive reasoning) is not, as will be shown later, quite clear. Induction (inductive reasoning) is defined, in essence, as "non-deduction" and is an even less clear concept. It is possible, however, to indicate a relatively definite "core" of inductive modes of reasoning. It includes, in particular, incomplete induction, inductive methods for establishing causal relationships, analogy, the so-called inverted laws of logic, etc.
The persuasiveness of inductive generalizations depends on the number of cases cited in support. The broader the base of the induction, the more plausible the inductive conclusion. But sometimes, even with a sufficiently large number of confirmations, the inductive generalization still turns out to be erroneous.
Verification and falsification. The problem of criticism of put forward hypotheses and theories requires special attention. If criticism directed at their refutation is based on empirical data, then, one might say, it is directly related to the topic of their empirical justification.
Falsification, or empirical refutation, manifests itself through the procedure of establishing falsity or logical verification.
According to modern logic, two interrelated operations - confirmation and refutation - are essentially unequal. One contradictory fact is enough to definitively refute a general statement, and at the same time, an arbitrarily large number of confirming examples is not able to confirm such a statement once and for all, to turn it into truth.
The principle of falsification is the law of classical logic, which was formed in the late XIX - early XX centuries. he was completely untouched by the criticism of logic, which began in the 1920s and became especially active in the 1950s. 20th century This law is accepted in all known non-classical logical systems that claim to be a more adequate description of the relation of logical consequence.
Falsification as a procedure includes two stages:
* establishing the truth of the conditional relationship "if A, then B", where B is an empirically verifiable consequence;
* establishing the truth "wrong B", i.e. falsification of B. Failure to falsify means failure to establish the falsity of B. The result of this failure is a probabilistic judgment “It is possible that A is true, i.e. AT". Thus, the failure of falsification is an inductive reasoning that has a scheme:
"if it is true that if A, then B, and not-B is false, then A" ("if it is true that if A, then B, and B, then A")
This scheme coincides with the indirect verification scheme. The failure of falsification is, however, a weakened verification: in the case the usual indirect verification assumes that premise B is a true statement; in a failed falsification, this premise is only a plausible assertion. Thus, the decisive but unsuccessful critique, which Popper highly appreciates and which he opposes as an independent method of verification, is in fact only a weakened version of verification.
Positive justification is the usual indirect empirical verification, which is a kind of absolute justification. Its result is: "Statement A, the consequence of which was confirmed, is justified." Critical justification is justification through criticism; his result: "Proposition A is more acceptable than its counterposition B, since A has withstood more severe criticism than B." Critical justification is comparative justification: just because statement A is more resistant to criticism and therefore more justified than statement B does not mean that A is true or even plausible.
2.Practical part.
2.1. Example #1.
1) Type of compatibility: equivalence (identity) - they differ in their content, but the volumes are the same.
Advance payment (A) - the amount of money issued against future payments for material assets, work performed and services rendered.
Deposit (B) - the amount of money issued by one of the parties to the contract to the other party on account of due payments.
2) Type of compatibility: crossing - the volumes partially coincide, i.e. contain common elements.
Director (A) - the head of an institution, enterprise, educational institution.
Accountant (B) - accounting specialist; accountant (in small enterprises, the duties of an accountant can be performed by a director).
3) Type of compatibility: subordination (subordination) - the scope of one concept is fully included (included) in the scope of another concept, but does not exhaust it.
Tax (A) - mandatory and non-equivalent payments paid by taxpayers to the budget of the corresponding level and state off-budget funds on the basis of federal laws on taxes and acts of the legislative bodies of the constituent entities of the Russian Federation.
Value added tax (V) is a type of value added tax. The object of taxation is the difference between the proceeds received from the sale of goods or the provision of services and the cost of purchases from various suppliers.
4) Type of incompatibility: subordination (coordination) is the relationship of two or more concepts that exclude each other, but belong to some more general generic concept.
Payment order (A) - a settlement document containing a written instruction from the payer to the bank to transfer a certain amount from his account to the beneficiary's account.
Payment request (B) - a settlement document containing the requirement of the recipient of funds to the payer to pay a certain amount through the bank.
Settlement documents (C) - registration in writing of the requirement or instruction of associations, enterprises, organizations for the transfer of funds in a non-cash manner.
5) Type of incompatibility: opposite (contrast) - the volumes of two concepts that are species of the same genus, and moreover, one of them contains some signs, and the other not only denies these signs, but also replaces them with others that exclude .
Debtor (A) - a legal or natural person who has a monetary or property debt to an enterprise, organization or institution.
Creditor (B) - a legal or natural person to whom the enterprise has a debt.
2.2. Example #2
Check (A) - a monetary document of the established form, containing an unconditional order of the drawer of the check to a credit institution to pay the holder of the check the amount specified in it.
Invoice (B) - a document indicating the amount of money due for payment for the sold goods or services rendered.
Financial document (C) - a business paper that legally confirms certain rights of its owner.
2.3. Example #3
Audit - financial analysis, accounting control, audit of the financial and economic activities of enterprises, organizations, firms, joint-stock companies, carried out by independent services of qualified specialists (audit services, auditors).
Let's generalize and limit the concept of audit in Table 1.
Table number 1.
Audit.
|
Generalization |
Limitation |
|
The financial analysis |
Mandatory audit |
|
Accounting control |
Initiative audit |
|
Audit of the financial and economic activities of the enterprise |
Audit of automated accounting systems Compliance audit Operational audit |
2.4. Example number 4.
A - No entrepreneur can not pay taxes (true),
E - Entrepreneur may not pay taxes (false),
I - Some entrepreneurs cannot avoid paying taxes (true),
A - Some entrepreneurs may not pay taxes (false).
The relation of logical subordination: A and I, E and O - the truth of the general judgment is determined by the truth of the particular, subordinate judgment. But the falsity of the general proposition leaves the particular proposition indeterminate.
The relation of partial coincidence (sub-contrast): I and O - have the same subjects and the same predicates, but differ in quality.
Opposite (contrast) ratio: A and E.
The relation of contradiction (contradiction): A and O, E and I - two contradictory judgments cannot be both true and false at the same time.
2.5. Example number 5.
Inference is a form of thinking in which, from one or more judgments, on the basis of certain rules, a conclusion, a new judgment is obtained, with the necessity or a certain degree of probability the following from them.
Conclusion.
Using arguments similar to those of A. A. Makarov, it is easy to conclude that not only logic, but also other sciences should have different interpretations (after all, logic underlies each of them). So, for example, from one point on the plane, you can draw an unlimited number of perpendiculars to one straight line, and parallel lines can intersect; the exception confirms the rule, even if there is no room for the rule under the heap of exceptions, and so on.
Getmanova and thousands of scientists like her do not recognize the simple fact that each specific question has a specific answer (truth is always specific). A person either knows him or he doesn't. The third is not given (although you can say the eightieth). And the fact that the comprehension of truth (truths) is infinite does not mean at all that specific knowledge can have an infinite gradation. Each established fact is marked by a truth value, and the accumulation of such facts leads to an increase in the number of concrete truths, but not to a qualitative change in some “abstract truth”.
The number of madness in the world is great and each madman has his own logic, his own physics, his own aesthetics, morality, morality, the concept of conscience and honor ... truth, usefulness, justice. own concept of progress. Why, then, any concepts at all, if they are different for everyone and the dialogue is based on their substitution? Some kind of limitless lecticism and a struggle of polymorphisms.
Bibliography.
1. Bocharov V.A., Markin V.I. Fundamentals of logic. Textbook. - M .: Infra - M, 2000. Rec.
2. Voishvillo E.K., Degtyarev M.G. Logics. Textbook. - M .: Vlados - Press, 2001. Rec.
3. Getmanova A.D. Logics. Textbook. - M .: Omega - L, 2002. Rec.
4. Ivanov E.A. Logics. Textbook. - M.: BEK, 2001
5. Ivlev Yu.V. Logics. Textbook. – M.: Logos, 1998, 2001. Rek
6. Kirillov V.I., Orlov G.A., Fokina N.I. Logic exercises. M., 2000. Rec.
7. Logic / A. A. Ivin. - M.: Higher School, 2004. - 304 p.
8. Logic: Textbook / Ruzavin G. I. - M .: UNITI, 2002. - 256 p.
9. Ogorodnikov V.P. Logics. Laws and principles of correct thinking. - St. Petersburg: Peter, 2004. Rec.
10. Textbook of logic. With a collection of problems / A. D. Getmanova. - 6th ed., revised. – M.: KNORUS, 2006. – 448 p.
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