Logics. Cheat sheet: briefly, the most important

Lecture notes, cheat sheets
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Logics. Cheat sheet: briefly, the most important

Lecture notes, cheat sheets

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1. SUBJECT AND SIGNIFICANCE OF LOGIC IN THE SYSTEM OF SCIENTIFIC KNOWLEDGE

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, logic - is the science of the methods and forms of correct thinking. The logical form of a specific thought is the structure of this thought, that is, the way in which its component parts are connected. Let us explain with an example the meaning of the concept “form of thinking”. Let's take two sentences: “All people are mortal” and “All rivers flow into the sea.” One of them is correct, the other is not. But they are the same in shape. Each one states something about a different subject. If we designate the object being spoken of by the letter S, and that which is being said by the letter P, we obtain the form of thought: all S are P; You can insert different content into it. Formal logic examines the basic forms of thinking: concept, judgment and inference, as well as the laws of their interrelation, by observing which one can obtain correct conclusions, provided that the initial provisions are true. 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. MAIN HISTORICAL STAGES IN THE DEVELOPMENT OF LOGIC

With the development of labor material and production activity of people, their mental abilities improved, and this led to the fact that thinking itself, its forms and laws, became the object of research.

Separate logical problems arose in the XNUMXst millennium BC. e. first in ancient India and China, and then in ancient Greece and Rome. Gradually, they are formed into a coherent system of knowledge, into an independent science.

The main reasons for the emergence of logic are the development of sciences and oratory. Science is based on theoretical thinking, involving inferences and evidence. Hence the need to study thinking itself as a form of cognition. Oratory manifested itself primarily in numerous court hearings as a mind-blowing power of persuasion, literally forcing listeners to incline to one opinion or another. Logic arises as an attempt to solve the mystery of this coercive power of speech.

In ancient Greece, logic was developed by Parmenides, Zeno, Democritus, Socrates, Plato. However, the founder of the science of logic is considered to be the greatest thinker of antiquity, a student of Plato - Aristotle (384-322 BC). He called his creation analytics, the term "logic" entered into scientific circulation later, in the III century. BC e.

After Aristotle in ancient Greece, logic was developed by the Stoics. Ancient Roman politicians Cicero and Quintilian, Arabic-speaking scientists - Al Farabi, Ibn Rushd, European medieval scholastics - U Ockham, P. Abelard.

In the era of modern times, the philosopher F. Bacon (15611626) published his study under the title "New Organon", it contained the foundations of inductive methods, improved later by D.S. Mill (1808-1873) and known as methods for establishing causal relationships between phenomena (Bacon-Mill methods).

In 1662 the textbook "Logic of Port-Royal" was published. Its authors P. Nicole and A. Arno created a logical doctrine based on the methodological principles of R. Descartes (1596-1650).

Logic, created on the basis of the teachings of Aristotle, existed until the beginning of the twentieth century. In the 1646th century Symbolic (mathematical) logic is actively developing, based on the idea of the German scientist and philosopher Leibniz (1716-1) about the possibility of reducing reasoning to calculations. This logic began to take shape in the middle of the 3th century. Its development is associated with the names of J. Boole, A.M. De Morgan, C. Pierce, G. Frege, Russian thinkers P.S. Poretsky and E.L. Bunitsky and others. The first major work on symbolic logic was the work of B. Russell and A. Whitehead “Principia Mathematika” in 1910 volumes, published in 1913-XNUMX. This work sparked a revolution in logic.

The ideas of dialectical logic go back to ancient and ancient Eastern philosophy, but only representatives of German classical philosophy gave them a finished form: Kant (1724-1804), Fichte (1762-1814), Schelling (1775-1854) and especially Hegel (1770-1831), who finally formulated the basic ideas of dialectics from the point of view of objective idealism.

Dialectical logic on a materialistic basis was developed by K. Marx, F. Engels, V. Lenin.

3. LOGIC AND LANGUAGE OF LAW

The specificity of the language of law lies in the uniformity of terms that should be used by different people in different cases and situations. Such terms are called legal. For example, in everyday life we can use the expression: "Petrov is a native Muscovite." The words "native Muscovite" are understood differently by different people. Some consider all those who were born in Moscow to be indigenous, others only those whose parents were Muscovites, others consider those who lived in Moscow for many years. Such indeterminacy of ordinary language is unacceptable in resolving legal issues. For example, a few years ago, a decision was adopted to put Muscovites living in communal apartments on the waiting list for a separate apartment. Who is entitled to this?

To avoid uncertainties, instead of ordinary words, legal terms are introduced through definitions: “A native Muscovite is a person who has lived in Moscow for 40 years.” There are two main ways to introduce legal terms. The first is by isolating one of the senses in which the expression is used in natural language, as in the above example. Another is to give the expression additional meaning compared to the generally accepted one. For example, “a crime is committed for the first time if it was actually committed for the first time, or the statute of limitations for prosecution for a previous crime has expired, or the criminal record has been withdrawn or expunged.” In this case, the scope of the term is expanded. In addition to legal terms, unspecified expressions are also used in the language of law. These are expressions that are given a precise meaning in other sciences, as well as those that are not ambiguous in ordinary language. In this case, these are expressions such as “live in Moscow”, “40 years”, “person”.

The language of law is subject to 3 normative principles:

1. The principle of objectivity. Something must be affirmed or denied about the meanings of the concepts included in the sentences, and not about the concepts themselves. For example, in the definition of V.I. Lenin: “Matter is a philosophical category for designating objective reality” remains unclear: Lenin called objective reality matter or just a category, i.e. the thought of objective reality.

2. The principle of unambiguity. A concept must designate only one object if it is singular. The concept general should denote objects of the same class.

3. The principle of interchangeability. If a part of a concept is replaced by another concept with the same meaning, then the meaning of the complex concept obtained as a result of such replacement must be the same as the meaning of the original concept. For example, the sentence “The Earth revolves around the Sun” is given. Let us replace the concept of “Sun” with the concept of “central body of the Solar System”. Obviously, the truth of the sentence has not changed. But if you make the same substitution in the sentence “Ptolemy believed that the Sun revolved around the Earth,” you will get a false sentence.

4. THE LAW OF IDENTITY AND ITS REQUIREMENTS FOR THINKING

Law of thinking, or logical law- this is a necessary, essential connection of thoughts in the process of reasoning.

The laws of thinking are formed independently of the will and desire of a person. Their objective basis is relative stability, qualitative certainty, interdependence of objects of reality. At the same time, reflecting certain aspects of reality, logical laws are not the laws of things themselves.

Among the many logical laws, logic identifies four main ones that express the fundamental properties of logical thinking - its certainty, consistency, consistency and validity. These are the laws of identity, non-contradiction, excluded middle and sufficient reason. They act in any reasoning, no matter what logical form it takes and no matter what logical operation it performs.

Law of Identity. Any thought in the process of reasoning must have a specific, stable content. This fundamental property of thinking expresses the law of identity: every thought in the process of reasoning must be identical to itself (a is a, or a = a, where a is any thought).

The law of identity can be expressed by the formula p ∞ p (if p, then p), where p is any statement, ∞ is the implication sign.

It follows from the law of identity: one cannot identify different thoughts, one cannot take identical thoughts for non-identical ones. Violation of this requirement in the process of reasoning is often associated with a different expression of the same thought in the language.

For example, two judgments: "N. committed theft" and "N. secretly stole someone else's property" - express the same idea (if, of course, we are talking about the same person). The predicates of these judgments are equivalent concepts: theft is the secret theft of someone else's property. Therefore, it would be erroneous to consider these thoughts as non-identical.

On the other hand, the use of ambiguous words can lead to erroneous identification of different thoughts. For example, in criminal law the word "fine" denotes a measure of punishment provided for by the Criminal Code, in civil law this word denotes a measure of administrative influence. Obviously, such a word should not be used in one sense.

The identification of different thoughts is often associated with differences in profession, education, etc. This happens in investigative practice, when the accused or the witness, not knowing the exact meaning of certain concepts, understands them differently than the investigator. This often leads to confusion, ambiguity, and makes it difficult to clarify the essence of the case.

The identification of different concepts is a logical error - a substitution of a concept, which can be both unconscious and deliberate.

Compliance with the requirements of the law of identity is important in the work of a lawyer, which requires the use of concepts in their exact meaning.

In any case, it is important to find out the exact meaning of the concepts used by the accused or witnesses, and to use these concepts in a strictly defined sense. Otherwise, the subject of thought will be missed and instead of clarifying the matter, it will be confused.

5. THE LAW OF NON-CONTRADICTION AND ITS SIGNIFICANCE IN HUMAN ACTIVITIES

Logical thinking is characterized by consistency. Contradictions destroy thought, complicate the process of cognition. The requirement of consistency of thinking expresses the formal-logical law of non-contradiction: two propositions that are incompatible with each other cannot be true at the same time; at least one of them must be false.

This law is formulated as follows: it is not true that a and not-a (two thoughts cannot be true, one of which denies the other). It is expressed by the formula ⌉(p ∧ ⌉p) (it is not true that p and not-p are both true). By p is understood any statement, by ⌉p is the negation of the statement p, the sign ⌉ in front of the whole formula is the negation of two statements connected by the conjunction sign ∨.

The law of non-contradiction applies to all incompatible judgments.

There will be no contradiction between judgments if one of them affirms that the object belongs to one attribute, and the other denies that another attribute belongs to the same object, and if we are talking about different objects.

This law is called the law of contradiction. However, the name - the law of non-contradiction - more accurately expresses its real meaning.

There will be no contradiction if we affirm something and deny the same thing regarding one subject, but considered at different times and (or) in different circumstances.

One and the same object of our thought can be considered in different ways. So, about student K.

we can say that he knows the German language well, since his knowledge satisfies the requirements for entering the institute. However, this knowledge is not enough to work as a translator. In this case we have the right to say: "K. knows German poorly." In two judgments, K.'s knowledge of the German language is considered from the point of view of different requirements, therefore, these judgments also do not contradict each other.

The law of non-contradiction expresses one of the fundamental properties of logical thinking - consistency, consistency of thinking.

One of the main requirements for a version in a forensic study is that, when analyzing the totality of factual data on the basis of which it is built, these data do not contradict each other and the version put forward as a whole. The presence of contradictions should attract the most serious attention of the investigator. But there are cases when the investigator, having put forward a version that he considers plausible, does not take into account the facts that contradict this version.

During the trial, the prosecutor and the defender, the plaintiff and the defendant put forward positions that contradict each other, defending their arguments and challenging the arguments of the opposite side. It is necessary to carefully analyze all the circumstances of the case so that the final decision of the court is based on reliable and consistent facts.

Among the circumstances under which the verdict is recognized as inappropriate to the actual circumstances of the case, criminal procedural law includes significant contradictions contained in the conclusions of the court set out in the verdict.

6. THE LAW OF THE EXCLUDED THIRD AND ITS ROLE IN KNOWLEDGE

The law of non-contradiction applies to all incompatible judgments. It establishes that one of them must be false. The question of the second proposition remains open: it may be true, but it may also be false.

The law of the excluded middle applies only to contradictory (contradictor) judgments. It is formulated as follows: two contradictory propositions cannot be false at the same time, one of them must be true: a is either b or not-b. Either the statement of a fact is true, or its negation.

Contradictory (contradictory) are judgments, in one of which something is affirmed (or denied) about each object of a certain set, and in the other - something is denied (asserted) about some part of this set. These judgments cannot be both true and false: if one of them is true, then the other is false, and vice versa. For example, if the proposition "Every citizen of the Russian Federation is guaranteed the right to receive qualified legal assistance" is true, then the proposition "Some citizens of the Russian Federation are not guaranteed the right to receive qualified legal assistance" is false. Contradictory are also two judgments about one subject, in one of which something is affirmed, and in the other the same thing is denied. For example: "P. was brought to administrative responsibility" and "P. was not brought to administrative responsibility." One of these judgments is necessarily true, the other is necessarily false.

This law can be written as follows: р ∨ ⌉р.

Like the law of non-contradiction, the law of the excluded middle expresses the consistency, consistency of thinking, does not allow contradictions in thoughts. At the same time, acting only in relation to contradictory judgments, he establishes that two contradictory judgments cannot be not only simultaneously true (as indicated by the law of non-contradiction), but also simultaneously false: if one of them is false, then the other must be true, There is no third.

Of course, the law of the excluded middle cannot indicate which of these judgments is true. This issue is resolved by other means. The significance of the law lies in the fact that it indicates the direction in the search for truth: only two solutions to the problem are possible, and one of them (and only one) is necessarily true.

The law of the excluded middle requires clear, definite answers, indicating the impossibility of answering the same question in the same sense both "yes" and "no", the impossibility of looking for something in between affirming something and denying the same.

This law is of great importance in legal practice, where a categorical solution of the issue is required. The lawyer must decide the case in the form of "either - or." This fact is either established or not established. The accused is either guilty or not guilty. The law knows only: "either-or".

7. THE LAW OF Sufficient Reason and Its Role in Cognition

The requirement of proof, the validity of thought expresses the law of sufficient reason: every thought is recognized as true if it has a sufficient basis. If there is b, then there is also its base a.

A person's personal experience can be a sufficient basis for thoughts. The truth of some judgments is confirmed by their direct comparison with the facts of reality. So, for a person who witnessed a crime, the justification for the truth of the proposition "N. committed a crime" will be the very fact of the crime, of which he was an eyewitness. But personal experience is limited. Therefore, a person in his activity has to rely on the experience of other people, for example. on the testimony of eyewitnesses of an event. Such grounds are usually resorted to in investigative and judicial practice in the investigation of crimes.

Thanks to the development of scientific knowledge, a person is increasingly using the experience of all mankind as the basis of his thoughts, enshrined in the laws and axioms of science, in the principles and provisions that exist in any field of human activity.

The truth of laws, axioms has been confirmed by the practice of mankind and therefore does not need new confirmation. To confirm any particular case, it is not necessary to substantiate it with the help of personal experience. If, for example, we know the law of Archimedes, then there is no point in proving it. The law of Archimedes will be a sufficient basis for confirming any particular case.

Thanks to science, which in its laws and principles consolidates the socio-historical practice of mankind, in order to substantiate our thoughts, we do not each time resort to checking them, but justify them logically, by deriving from already established provisions.

In this way, a sufficient basis for any thought can be any other, already verified and established thought, from which the truth of this thought necessarily follows.

If the truth of proposition a implies the truth of proposition b, then a will be the reason for b, and b the consequence of this reason.

Validity - the most important property of logical thinking. In all cases when we affirm something, convince others of something, we must prove our judgments, give sufficient reasons confirming the truth of our thoughts. This is the difference between scientific and non-scientific thinking, which is characterized by lack of evidence, the ability to accept various positions and dogmas on faith.

The law of sufficient reason is incompatible with various prejudices and superstitions. It is of great theoretical and practical importance. Fixing attention on the judgments that justify the truth of the put forward provisions, this law helps to separate the true from the false and come to the right conclusion.

Any conclusion of the court or investigation must be substantiated. In the materials concerning any case, containing, for example, the assertion of the guilt of the accused, there must be data that is a sufficient basis for the accusation.

8. CONCEPT AS A FORM OF THINKING

A concept is a form of thinking that reflects objects in their essential features.

A feature of an object is that in which objects are similar to each other or in which they differ from each other. Everything that characterizes an object in one way or another allows us to consider it precisely as a given object, and not another, and serves as its sign for a person (i.e., an indicator, a sign, a means of recognizing the object).

Signs of an object can be of the most diverse nature. They can be general and single, essential and insignificant, necessary and accidental. The concepts are based on general, essential and necessary features. The concept is of an objective nature, i.e., it reflects the things, processes, phenomena, their properties, connections and relations that are concretely existing in the material or spiritual activity of people. At the same time, concepts are relatively independent. The subject may disappear, but the concept of it can be preserved and passed on from generation to generation. With the change in human activity, new concepts appear.

Concepts are fixed and expressed in words and phrases. The unity of the concept and the word does not mean their complete coincidence. Concepts are unambiguous, and words often have many meanings. Every language has homonyms and synonyms. Homonyms are words that coincide in sound and form, but express different concepts (for example, the word "braid" means a strand of hair, a narrow strip of land, a tool for cutting grass, etc.). Synonyms - words that are close or identical in meaning, but different in sound (for example, homeland and fatherland, illness and disease, legal science - jurisprudence, etc.).

In different national languages, the same concept is expressed in different words.

Concepts serve as one of the most important ways of spiritual mastering of the world by man. They perform two main functions.

The first is educational. The concept is formed as a result of revealing the most general properties of objects, i.e., already in the process of their formation, concepts help to comprehend the general properties of objects, and therefore, to cognize their essence. Concepts serve as a means of further knowledge of the world by a person with the help of a logical operation of subsuming an object under a concept. For example, the concept of "substance" was formed as a result of highlighting the general properties of objects in the surrounding world. In the future, it was extended to new phenomena, allowing them to distinguish properties already known to man.

The second is communicative, which consists in the fact that the concept is a means of communication. Consolidating their knowledge in the form of concepts, people then exchange them in the process of communication, and also pass them on to subsequent generations. Thus, the social inheritance of knowledge is carried out, the spiritual continuity of generations is ensured.

9. LOGICAL TECHNIQUES FOR THE FORMATION OF CONCEPTS

The formation of a concept is not a simple mirror act of reflecting the objects of reality, but a most complex dialectical process. It involves the activity of the researcher and includes many logical techniques, the most important of which are analysis and synthesis, comparison, abstraction and generalization.

The selection of features is associated with the mental division of objects into its constituent parts, sides, elements.

The mental breakdown of an object into parts is called analysis..

Elements, sides, features of the subject, identified through analysis, must be combined into a single whole. This is achieved with the help of a technique opposite to analysis - synthesis.

Synthesis - this is a logical technique with the help of which the mental connection of parts of an object dissected by analysis is carried out.

Comparison - mental comparison of one object with another, identifying signs of similarity and difference in one way or another.

Abstraction - mental simplification of objects by highlighting some features in them and abstracting from others, the result of this process is called abstraction or concept.

Generalization - mental association of homogeneous objects, their grouping based on certain common characteristics. Thanks to generalization, the essential features identified in individual objects are considered as signs of all objects to which this concept is applicable.

Thus, establishing the similarity (or difference) between objects (comparison), dividing similar objects into elements (analysis), highlighting essential features and abstracting from non-essential ones (abstraction), connecting essential features (synthesis) and extending them to all homogeneous objects (generalization), we form one of the main forms of thinking - the concept.

10. CONTENT AND SCOPE OF THE CONCEPT

The concept is the simplest form of thinking, but it has a complex structure, that is, it consists of elements that are connected in a certain way. The concept differs content и volume.

The content of a concept is the totality of essential features of an object, which is conceived in this concept. For example, the content of the concept of “crime” is the following characteristics: socially dangerous nature of the act, illegality, guilt, punishability. The content of a concept can be schematically expressed as follows: A(BCDs), where A is any concept in general, and BCDs are the attributes of objects conceivable in it.

The scope of a concept is the set of objects that is conceived in the concept. The scope of the concept “crime” covers all crimes, since they have common essential features. Graphically, the scope of a concept is depicted by a circle, where A is any concept.

The objects included in the scope of the concept are called by class or many. A class is made up of subclasses or subsets. For example, the class of phenomena covered by the concept of “law” includes such subclasses (subsets) as historical forms of law - slave, feudal, bourgeois, etc., its various branches - labor, civil, criminal, etc.

An individual item belonging to a class of items is called an element. For example, criminal, civil, labor law are elements of the “law” class.

Distinguish a universal class, a unit class, and a null or empty class. A class consisting of all elements of the domain under study is called a universal class, eg. class of planets of the solar system, class of cities of the world, academies or universities.

Single class - a class consisting of one subject: planet Earth, city of Moscow, etc.

An empty (null) class does not contain a single item (centaur, perpetual motion machine, round square).

11. THE LAW OF INVERSE RELATIONSHIP BETWEEN THE CONTENT AND VOLUME OF THE CONCEPT. CLASSIFICATION OF CONCEPTS BY VOLUME

The content and scope of the concept are organically linked. A certain content of a concept corresponds to its specific volume and vice versa. A pattern can be traced in their relationship: with a decrease in the volume of a concept, its content becomes richer, since the number of features in it increases, and vice versa, with an increase in the volume, the number of features decreases. This pattern has been called the law of the inverse relationship between the volume and content of a concept. Its action extends to such concepts, of which one acts as a subclass or element of another and manifests itself in the process of such logical operations as generalization and limitation of concepts.

Increasing the content of the concept of "state" by adding a new feature - "modern", we move on to the concept of "modern state", which has a smaller volume. Increasing the volume of the concept "textbook on the theory of state and law", we pass to the concept of "textbook", which has less content.

In terms of volume First of all, empty and non-empty concepts are singled out.

empty are called concepts whose volume is equal to zero. These include concepts that are mythological in nature (centaur, mermaid), concepts whose scientific failure has come to light over time (caloric, phlogiston, perpetual motion machine), as well as concepts about something that does not really exist, but is possible (an extraterrestrial civilization, aliens).

Until recently, the concept of "President of Russia" belonged to such concepts.

Non-empty concepts have a scope that includes at least one real object. Non-empty concepts are divided into singular and general.

If the volume of a concept is only one object of thought, then it is called single, eg. Sun, Earth, Russia, etc. Units are concepts that relate to a collection of objects, if this collection is thought of as a single whole: the Solar system, humanity, the UN, etc.

General concepts include in their scope a group of objects, and they are applicable to each element of this group (star, planet, state). General concepts can be registering and non-registering.

registering are called concepts in which the set of elements conceivable in them can be taken into account, registered at least in principle, for example. the concepts "participants of the Great Patriotic War", "planet of the solar system", "relatives of the victim Shilov". The registering concepts have a finite scope.

A general concept referring to an indefinite number of elements is called non-registering. For example, in the concepts of “person”, “investigator”, “decree”, the many elements conceivable in them cannot be taken into account; all people, investigators, decrees of the past, present and future are conceived in them. Non-registering concepts have an infinite scope.

12. CLASSIFICATION OF CONCEPTS BY CONTENT

According to the content All concepts are divided into four groups.

▪ Positive and negative

Positive concepts are called, the content of which is the properties inherent in the subject. For example, competent, orderly. Negative concepts are called, the content of which indicates the absence of certain properties of the object. E.g., illiterate, disorder. In Russian, such concepts often begin with the prefixes "ne-" or "bez-". In words of foreign origin with a negative prefix - a-: anonymous, asymmetry. It should be noted that not all words of the Russian language that begin with non- and without- contain negation of signs, for example. bauble, indignation.

▪ Collective and non-collective Collective are called concepts in which the signs of a certain set of elements that make up a single whole are thought, for example. collective, regiment, constellation. The content of a collective concept cannot be attributed to each individual element included in its scope, it refers to the entire set of elements. For example, the essential features of a team (a group of people united by a common work, common interests) are not applicable to each individual member of the team. Collective concepts can be general (collective, regiment, constellation) and singular (collective of our institute, constellation Ursa Major). Non-collective are called concepts in which the signs related to each of its elements (star, state, region) are thought. In the process of discussion, general concepts can be used in a divisive and collective sense. For example, the concept of "man" in the sentence "A man explores space" has a collective meaning, because it does not apply to each person individually, and in the sentence "A man has the right to citizenship" has a divisive meaning, because it refers to each to a person.

▪ Concrete and abstract concepts

A concept is called concrete in which an object or a set of objects is conceived as something independently existing (a book, a witness, a state). Specific concepts can be both general and singular. An abstract concept is a concept in which a sign of an object or a relationship between objects is conceived (courage, responsibility, whiteness, friendship, mediation). Abstract concepts can be general (mediation, whiteness) or singular (Einstein's genius).

▪ Non-relative and correlative concepts Irrelevant are concepts that reflect objects that exist separately and are thought outside their relationship with other objects (student, state, law). Correlative concepts are those that contain signs indicating the relationship of one concept to another (parents - children, boss - subordinate, plaintiff - defendant).

Knowledge of the types of concepts - one of the necessary conditions that ensure the accuracy and clarity of thinking. To operate with a concept, it is necessary not only to clearly know its content and scope, but also to be able to give it a logical description. For example, a lawyer is a general (non-registering), non-collective, concrete, positive, irrelevant concept.

13. RELATIONS BETWEEN CONCEPTS

According to the content, there can be only two types of relations between concepts - comparability and incomparability. Concepts that are far from each other in their content and do not have common features are called incomparable (romance and brick). There is no logical relationship between them.

Comparable concepts - these are concepts that have in their content common, essential features (by which they are compared). For example, law and morality. Relationships between concepts are depicted using schemes - Euler circles. Between comparable concepts, two types of relations are possible in terms of volume: compatibility and incompatibility.

Compatible concepts - these are those whose volumes completely or partially coincide. The following relations are formed between compatible concepts:

1 - equal volume. Concepts that differ in their content, but whose volumes are the same, are called equivolume or equivalent. For example, “L.N. Tolstoy” - A and “author of the novel “War and Peace” - V. The volumes of identical concepts are depicted by circles that completely coincide.

2 - crossing. Concepts whose scopes partially coincide are called intersecting, for example. "student" and "athlete", "lawyer" and "writer". They are depicted as intersecting circles. In the intersecting part of the two circles, students are thought of as athletes. On the left side of the circle we think of students who are not athletes, and on the right side we think of athletes who are not students.

3 - submission. In relation to subordination (subordination), concepts are found if the scope of one is completely included in the scope of the other, but does not exhaust it. This is the relationship of species - B and genus - A (mammal and cat).

Incompatible concepts are called, the volumes of which do not coincide. Incompatible concepts can be among themselves in the following relations.

1 - subordination. In relation to subordination (coordination) there are concepts whose scopes are mutually exclusive, but belong to some more general generic concept. For example, “spruce” - B, “birch” - C belong to the scope of the concept “tree” - A. They are depicted as non-intersecting circles inside a common circle. These are species of the same genus.

2 - opposite. In relation to the opposite (contrary) there are two concepts, the signs of which contradict each other, and the sum of their volumes does not exhaust the generic concept (bravery - cowardice).

3 - contradiction. In relation to contradiction (contradictoryity), there are two concepts that are species of the same genus, and at the same time, one concept indicates some signs, and the other denies these signs, excludes them, without replacing them with any others (for example, A - white paint , then the concept that is in a relationship of contradiction with it should be designated non-A (not white paint).The Euler circle in this case is divided in half and there is no third concept between them.

14. LOGICAL OPERATION OF GENERALIZATION AND LIMITATIONS OF CONCEPTS

Of great importance for achieving the certainty of our thinking are the logical operations of generalization and limitation of concepts, based on the law of the inverse relationship between the content and scope of the concept.

Generalize the concept - means to move from a concept with a smaller volume, but a large content to a concept with more volume but less content. For example, generalizing the concept of "city court", we get the concept of "court", the scope of the new concept is wider than the original, since the first relates to the second as a species to a genus. At the same time, the content of the new concept has decreased, since we have excluded its specific features. Generalization of the concept can be multi-stage, for example. "criminal offence", "crime", "wrongful act", "act". However, the generalization of concepts cannot be infinite. The limit of generalization is categories - concepts with an extremely wide scope: matter, consciousness, movement, property, etc. Categories do not have a generic concept.

Restricting a concept is the opposite of generalization.

Restrict concept - means moving from a concept with a larger volume, but less content, to a concept with a smaller volume, but more content. For example, “lawyer”, “investigator”, “investigator of the prosecutor’s office”, “investigator of the prosecutor’s office Petrov”. The limit of limitation of a concept is a single concept.

The logical operations of generalizing and restricting concepts are widely used in the practice of thinking: moving from the concept of one volume to the concept of another volume, we clarify the subject of our thought, make our thinking more defined and consistent.

Generalization and limitation of concepts must not be confused with a mental transition from a part to a whole and the separation of a part from a whole. For example, a day is divided into hours, hours into minutes, minutes into seconds. Each subsequent concept is not a kind of the previous one, which in turn cannot be considered as generic. Therefore, the transition from the concept of "hour" to the concept of "day" is not a generalization, but a transition from part to whole.

15. TYPES OF DEFINITIONS

By function, which definitions carry out in the process of cognition, they are divided into nominal and real.

Nominal (from lat. nomen - name) is called a definition, through which a new name is introduced, it, as it were, expresses the requirement to call a certain object with this term. For example, "The term "legal" means pertaining to jurisprudence, legal". Such a definition can be characterized in terms of efficiency, expediency.

real a definition is called, revealing the essential features of an object, describing an object. For example, "evidence is proof of the guilt of the accused of a crime." Real definitions must correctly reflect the subject, they can be characterized in terms of truth.

According to the method of revealing the content of the concept definitions are divided into explicit and implicit.

Explicit definitions reveal the essential features of the subject, they establish a relationship of equality, equivalence between the defined and the defining.

The most common is the definition through the nearest genus and specific difference. For example, "theft is the secret theft of someone else's property." The concept of "theft" is brought under the closest generic concept - "theft of another's property", and then within the framework of this genus, a distinctive feature of theft from other types of theft is revealed: robbery, robbery, that this theft is secret. The structure of this type of definition is expressed by the following formula:

A \uXNUMXd Sun,

where A is the concept being defined; B - genus; c - species difference.

This type of definition has the following varieties:

a) genetic definition. It reveals the origin of the item. For example, "A custom is a rule of conduct that has developed as a result of its actual application for a long time";

b) essential definition (or definition of the quality of the subject). It reveals the essence of the object, its nature or quality. It is widely used in all sciences;

c) functional definition. It reveals the purpose of the subject, its role and functions. For example, "A thermometer is a device for measuring temperature";

d) structural definition (or compositional definition). It reveals the elements of the system, types of any kind or part of the whole. For example, "The political system is a combination of state and non-state, party and non-party organizations and institutions."

Definition through genus and specific difference has a limitation. It is not applicable to categories that do not have a genus, and to single concepts, since it is impossible to indicate a specific difference for them. Correlative definitions (definition through opposition) are used to define categories. For example, "Freedom is a recognized necessity."

For single concepts, one usually uses implicit definitions, which include descriptions, characteristics, comparisons, contextual, ostensive (using display), etc.

16. RULES FOR DEFINITION OF CONCEPTS

The correctness of the definition depends on the structure of the concept, which is governed by logical rules.

1. The definition must be proportionate

The volume of the concept being defined must be equal to the volume of the defining one, i.e. they must be of equal volume - A \uXNUMXd Bs. For example, "A debut is the first performance of an artist in front of an audience."

If this rule is violated, two kinds of errors are possible. If the defining concept has a wider scope than the defined one, then this is called the error of too broad definition (A < Bc). For example, "A debut is an artist's performance in front of an audience."

If the defining concept is narrower in scope than the defined one, then this is called the error of too narrow a definition (A > Bc). For example, "The debut is the first performance of the artist in front of the public of a big city."

2. The definition must not contain a circle

If, in defining a concept, we resort to another concept, which, in turn, is defined with the help of the first one, then such a definition contains a circle. For example, the erroneous definition of law as a system of norms, which has the task of protecting the existing legal order, and the definition of the rule of law, in turn, through the concept of law.

A kind of circle in the definition is a tautology (from Greek - the same word) - an erroneous definition in which the defining word repeats the defined. For example, "A careless crime is a crime committed through negligence."

3. The definition must be clear

It should indicate known features that do not need to be defined and do not contain ambiguity. If, however, a concept is defined in terms of another concept whose attributes are unknown and which itself needs to be defined, then this leads to an error called the definition of the unknown in terms of the unknown, or the definition of x in terms of y. For example, "Indeterminism is a philosophical concept opposite to determinism." Before defining the concept of "indeterminism", it is necessary to define the concept of "determinism". The rule of clarity warns against replacing the definition with metaphors, comparisons, etc., which, although they help to get an idea of the subject, do not reveal its essential features.

4. Definition must not be negative

A negative definition indicates features that do not belong to the subject, but does not indicate features that belong to the subject. For example: "A whale is not a fish", "Comparison is not a proof".

17. LOGICAL OPERATION OF DIVISION OF CONCEPTS. TYPES OF DIVISION

A logical operation that reveals the scope of a concept is called division. Division allows us to identify the range of objects to which this concept applies; this is the division of the genus into species. Genus-species relationships are characterized by the fact that what can be said about the genus can also be said about the species. Thus, the concept of “constitution” can be divided into the constitution of a federal state and the constitution of a unitary state. These concepts have the same characteristics as the generic concept.

Division must be distinguished from mental dismemberment. Dismemberment refers to the relationship of the whole and the part. Thus, the constitution is divided into articles and paragraphs that do not have the features of the concept of "constitution".

Division is necessary in the following cases:

1) when it is necessary to reveal not only the essence, but also the forms of its manifestation;

2) when it is necessary to outline the scope of the concept;

3) in case of polysemy of the term.

The division has its own structure. It differs:

▪ dividend - this is a generic concept, the scope of which is revealed through its constituent types (in our example, this is the constitution);

▪ division members - types of generic concept obtained as a result of the operation itself (the constitution of a unitary state, the constitution of a federal state);

▪ base of division - the sign (or signs) on which this operation is performed (in our case, this is the nature of the state structure).

There are two types of division: according to the modification of the attribute and dichotomous.

1 - division by modification of the characteristic underlying the division. For example, all people can be divided into groups according to various criteria: racial, social, professional, gender, age, territorial, etc. In each of these cases, the members of the division will be different. This type of division is often used in science and legal practice. However, the disadvantage of this type of division is that the volume of the generic concept being divided may be inexhaustible.

2 - dichotomous division (from the Greek words dicha - into two parts and tome - section) represents the division of the volume of the dividing concept into two contradictory concepts. For example: nature is divided into living and nonliving, chemical elements into metals and non-metals, etc. The advantage of this type of division is that the scope of the dividing concept is completely exhausted, but its disadvantage is that the area of the negative concept remains quite vague.

Sometimes a mixed division is used. For example, citizens are divided into capable and incapacitated, and then capable, in turn, are divided into fully and partially capable.

18. RULES OF DIVISION

Like the definition, the division operation is subject to special rules.

1. Division should be carried out on only one basis. This requirement means that the individual characteristic or set of characteristics chosen initially as the basis should not be replaced by other characteristics during the division. It is correct, for example, to divide the climate into cold, temperate and hot. Dividing it into cold, temperate, hot, maritime and continental will no longer be correct: at first the division was made by average annual temperature, and then by humidity. This error is called cross division or misdivision.

2. The division must be proportionate or exhaustive, i.e. the sum of the volumes of the division terms must be equal to the volume of the concept being divided. This requirement prevents you from omitting individual division terms. If, for example, when dividing crimes depending on the nature and degree of public danger, crimes of minor gravity, moderate gravity and serious crimes are distinguished, then the rule of proportionality will be violated, since another member of the division is not indicated - especially dangerous crimes. This division is called incomplete.

The rule of proportionality will also be violated if extra members of the division are indicated, i.e., concepts that are not species of this genus. For example, if, when dividing the concept of "criminal punishment", in addition to all types, a warning is indicated that is not included in the list of penalties in criminal law, but is a type of administrative penalty, then this will be a mistake, which is called division with extra members.

3. Division terms must be mutually exclusive.

They can only be incompatible, subordinate concepts. For example, divisions are incorrect: students are divided into excellent students, underachievers and achievers, since the concepts of an excellent student and a successful student do not exclude each other; crimes are divided into intentional, careless and military, because military can be either intentional or careless at the same time.

4. Division must be consistent and continuous. One should move from the genus to the nearest species, and then from them to the nearest subspecies. If this rule is violated, a logical error occurs - a jump in division. So, if we first divide the law into branches - labor, criminal, civil, and then civil - into the right of ownership, the law of obligations, the law of inheritance, then this is a correct, consistent and continuous division. But if, after labor and criminal law, we immediately name inheritance law, then this will mean a leap in division.

19. CLASSIFICATION. JUDGMENT: ESSENCE AND ROLE IN KNOWLEDGE

Classification - this is a special kind of division, which is the distribution of objects into groups (classes), in which each class has its own permanent, specific place. The classification differs in a number of properties.

▪ This is a division or a system of successive divisions, which are made in terms of characteristics that are essential for solving a theoretical and practical problem. For example, on the basis of atomic weight, Mendeleev’s periodic table of elements was created. When making a classification, it is important to take into account its purpose, i.e. indicate which problems it contributes to.

▪ When classifying, it is necessary to distribute objects into groups in such a way that one can judge their properties by their place in the classification (for example, by the place of a chemical element in Mendeleev’s periodic system one can judge its properties).

▪ The classification results can be presented in the form of tables or diagrams.

When creating classifications, it is important to take into account their relative nature, since the classification can often not take into account the transitional forms of the phenomenon. In addition, it may become outdated.

In addition to the considered classification, called scientific, in everyday life the so-called. artificial classification, i.e., the distribution of objects into classes according to insignificant features, for example, the distribution of surnames in alphabetical order.

Judgment - this is a form of thought through which the presence or absence of any connections and relationships between objects is revealed.

The hallmark of judgment is the affirmation or denial of something about something. The judgment may be true or false. The truth of a judgment is determined by its correspondence to reality, it does not depend on our attitude towards it and is objective. The truth of judgments about the simplest everyday situations is obvious and does not require special research. In science, it took years of hard work to confirm or deny any proposition. This also applies to legal practice.

All scientific truths are formulated in the form of judgments. They also serve as a universal form of spiritual communication between people, the exchange of information. The form of judgment is usually taken by articles of normative acts regulating the behavior of people in society.

Every proposition is expressed in a sentence, but not every proposition is a proposition. A judgment can be a sentence that communicates some information that is characterized as true or false, that is, it can only be a declarative sentence.

The same proposition can be expressed in different sentences. For example, "Aristotle is the founder of the science of logic" and "Educator A. Macedonian is the founder of the science of logic."

In turn, the same sentence can express different judgments. For example, the sentence "Aristotle is the founder of the science of logic" can express the following judgments: "Aristotle (and not anyone else) is the founder of the science of logic"; "Aristotle is the founder (and not the successor) of the science of logic"; "Aristotle is the founder of the science of logic (and not of physics or mathematics)."

20. LOGICAL STRUCTURE OF JUDGMENTS

The following elements can be distinguished in the judgment: subject, predicate, connective and quantifier.

The subject of judgment is the concept of the subject of judgment, what we judge; it contains the original knowledge. The subject is indicated by the letter S.

A predicate is the concept of an attribute of an object, what is said about the subject of judgment. The predicate contains new knowledge about the subject and is denoted by the letter Р. The subject and predicate are called in terms of judgment.

A copula expresses the relationship between the subject and the predicate.

The connective unites the terms of the judgment into a single whole, establishing whether or not the attribute belongs to the object.

A link can be expressed in one word (is, essence, is) or a group of words, or a dash, or a simple agreement of properties ("The dog barks", "It's raining").

quantifier or quantifier word ("all", "none", "some"), characterizes a judgment in terms of its quantity, indicates the relationship of the judgment to the entire volume of the concept expressing the subject, or to its part.

To reveal the logical meaning of a sentence, it is necessary to find a subject and a predicate in it. In simple cases, they correspond to the subject and predicate. In complex sentences, the subject can be expressed by the subject group, and the predicate - by the predicate group. For example, in the sentence "Anyone who has benefited from a crime is guilty of committing it" the subject is the subject group: "anyone who has benefited from the crime" because this is the initial information, and the predicate is the predicate group: "guilty in its commission", since this is new information.

But the correspondence of the subject with the subject, the predicate with the predicate is not always observed. In the sentence "An outstanding Russian writer is Sholokhov" the subject is "an outstanding Russian writer" and the predicate is "Sholokhov". The subject and predicate can also be expressed by other members of the sentence.

There are a number of ways to identify the subject and predicate in a sentence. First, we can specifically single out the subject of the judgment, which is the subject of the sentence. For example, "The place where the lawyer Petrov will speak is the court." In this sentence, the subject is the subject, which is emphasized by the introductory sentence. Secondly, the order of words in a sentence must obey the rule: everything known in the judgment is shifted towards the subject at the beginning of the sentence, and the predicate, as a carrier of novelty, is placed at the end. Thirdly, you can use logical stress. In oral speech, it is expressed by amplifying the voice, and in writing by underlining. Finally, it is very important to consider the context, which comes to the rescue in particularly difficult cases.

21. TYPES OF SIMPLE JUDGMENTS

A proposition that does not include other propositions is called simple.. They are a reflection of one single connection of the objective world, regardless of what this connection is in content. For example, “This is a man”; “The rose has a pleasant smell”, etc.

Simple judgments are varied in their manifestations. They are divided into types according to logical features: the nature of the link (quality and quantity) of the subject and the predicate, the relationship between the subject and the predicate.

On the basis of the relationship between the subject and the predicate, judgments are distinguished:

a) attributive (from lat. "property", "sign") - judgments about the attribute of an object. They reflect the connection between an object and its attribute; this connection is affirmed or denied. Attributive judgments are also called categorical, i.e. clear, unconditional. Logical scheme of attributive judgment S-PWhere S - the subject of judgment, Р - predicate, "-" - link. For example, "Counsel met with the accused." Categorical judgments are divided according to quality and quantity.

By quality, affirmative and negative judgments are distinguished.

Affirmative expresses belonging to an object of any property, negative - absence of any property, they differ in the quality of the binder.

A judgment with a negative predicate, but with an affirmative link, is considered as affirmative, for example, "This court decision is unreasonable."

By quantity, single, private and general judgments are distinguished. A quantitative characteristic is expressed by a general quantifier.

A single judgment is a judgment in which something is affirmed or denied about one thing..

For example, "This building is a monument of architecture."

A particular judgment is a judgment in which something is affirmed or denied about a part of objects of a certain class using the words some, many, few, majority, minority, part. For example, “Some of the crimes are economic.”

General is a judgment in which something is affirmed or denied about all objects of a certain class using the words all, no one, any, every. For example: “All the witnesses testified,” “No one came to the meeting.” Sometimes the quantifier is not indicated, and then it is determined by its meaning, for example, “Indifference humiliates”;

b) about relations between objects (so-called judgments with relations). These can be relations of equality, inequality, spatial, temporal, cause-and-effect, etc. For example: “A equals B,” “Kazan is east of Moscow,” “Semyon is the father of Sergei,” etc. The following symbolic notation of judgments with relations is accepted: xRуWhere х и у - members of the relation, they designate concepts about objects;

В - relationship between them. The entry reads: х is in relation R к у. Recording a negative judgment ⌉

(xwoo) (it is not true that х is in relation В к u);

at) existence, expressing the very fact of existence or non-existence of the subject of judgment. For example, “There are statistical laws.” The predicates of these judgments are the concepts of the existence or non-existence of an object.

22. UNIFIED CLASSIFICATION OF SIMPLE JUDGMENTS

Combining quantitative and qualitative characteristics, attributive judgments are divided into four groups: general affirmative, general negative, particular affirmative and particular negative.

general affirmative - is a judgment that is general in quantity and affirmative in quality. For example, “Everyone who commits a crime must be subjected to a fair punishment.” The scheme of such a judgment is "All S are Р", where the quantifier word “all” characterizes the quantity, the affirmative connective “essence” - the quality of the judgment.

general negative - judgment, general in quantity and negative in quality. For example, “No innocent person should be held criminally responsible.” The scheme of such a judgment is "Neither S alone is not P". The quantifier word “not one” characterizes quantity, the negative connective “is not” characterizes the quality of the judgment.

private affirmative - judgment, particular in quantity and affirmative in quality. For example, “Some court verdicts are guilty.” The scheme of such a judgment is "Some S are P". The quantifier word “some” indicates the quantity of the judgment, the affirmative connective expressed by the word “is” indicates its quality.

private negative - judgment is partial in quantity and negative in quality. For example, “Some court verdicts are not guilty.” The scheme of such a judgment is "Some S are not P". The quantifier word “some” indicates the quantity of the judgment, the negative connective “not” indicates its quality.

In logic, the abbreviated designation of judgments according to their combined classification is accepted: А - general affirmative judgments;

I - private affirmative;

Е - generally negative;

О - privately negative.

In the language of predicate logic, the considered judgments are written as follows:

А - (All S heart R);

Е - (Neither one S is not R);

I - (Some S are R);

О - (Some S are not P).

23. SELECTING AND EXCLUSIVE JUDGMENTS

A special place in the classification of judgments is occupied by distinguishing and excluding judgments.

Singling out judgments reflect the fact that the attribute expressed by the predicate belongs to (or does not belong) only to this and no other object.

Distinguishing judgments can be single, private and general. For example, "Only Zimin is a witness to the incident"

(S and only S is P - a single distinguishing proposition). It expresses the knowledge that Zimin is the only witness to the incident. The subject and predicate of this judgment have the same scope.

"Some cities are the capitals of states" - an example of a particular highlighting judgment (some S and only S are P). Only cities can be the capitals of states, and only a certain part of them. The predicate of a particular emphasizing judgment is completely included in the scope of the subject.

"All crimes, and only crimes prescribed by law, are socially dangerous acts" - an example of a general singling out judgment (All S, and only S, are P). The volumes of the subject and predicate of the general distinguishing judgment completely coincide.

The words "only", "only", which are part of sentences expressing highlighting judgments, can be placed both before the subject and before the predicate (for example, "Criminal punishment is applied only by a court verdict"). But they may not exist at all. In these cases, logical analysis helps to establish that this judgment is selective.

Exclusive is a judgment that reflects the belonging (or non-belonging) of a feature to all objects, with the exception of some part of them.. For example, “All students in our group, except Volkov, passed the exams.” Exclusive judgments are expressed by sentences with the words “except”, “except”, “besides”, “not counting”, etc.

(All S, with the exception of S', the essence is P).

The significance of distinguishing and excluding judgments lies in the fact that the provisions expressed in the form of these judgments are characterized by accuracy and certainty, which excludes their ambiguous understanding. For example, in the Constitution of the Russian Federation Art. 118 (part 1) and 123 (part 2) read: "Justice in the Russian Federation is carried out only by the court", "In absentia trial of criminal cases in courts is not allowed, except as provided for by federal laws."

24. DISTRIBUTION OF TERMS IN JUDGMENTS

In logical operations with judgments, it becomes necessary to establish whether its terms - subject and predicate - are distributed or not distributed.

The term is considered distributed, if it is taken in full.

The term is considered unallocated, if it is taken in part of the volume.

Consider how the terms are distributed in the judgments A, E, I, O.

Judgment A (All S are P). "All the students in our group (S) passed the exams (R)". The subject of this judgment (“the students of our group”) is distributed, it is taken in full: we are talking about all the students of our group. The predicate of this judgment is not distributed, since it represents only a part of the persons who passed the exams, coinciding with the students of our group.

Thus, in general affirmative judgments S distributed and Р not distributed. However, in general affirmative judgments, the subject and predicate of which have the same volume, not only the subject, but also the predicate is distributed. Such judgments include general discriminating judgments, as well as definitions that obey the rule of proportionality.

Judgment E (No S is a P). "Not a single student in our group (S) is not underachieving (R)". Both subject and predicate are taken in full. The scope of one term is completely excluded from the scope of the other: not a single student in our group is among the unsuccessful ones, and not a single unsuccessful student is a student in our group. Consequently, in generally negative judgments and Sand Р distributed.

Judgment I (Some S are P). "Some of the students in our group (S) - excellent students (R)". The subject of the judgment is not distributed, because only a part of the students in our group are thought of in it, the scope of the subject is only partially included in the scope of the predicate: only some students in our group are among the excellent students. But the scope of the predicate is only partially included in the scope of the subject: not all, but only some excellent students - students in our group. Consequently, in a private affirmative judgment neither SOr Р not distributed.

An exception to this rule is made by particular judgments, the predicate of which is completely included in the scope of the subject. For example, "Some parents, and only they (S), have many children (R)". Here the concept of “large families” is fully included in the scope of the concept of “parents”. The subject of such a judgment is not distributed, the predicate is distributed.

judgment about (some S not the point Р). "Some of the students in our group (S) - not excellent students (R)". The subject of this judgment is not distributed (only a part of the students in our group is thought), the predicate is distributed, all the excellent students are thought in it, not one of whom is included in that part of the students in our group that is thought in the subject. Therefore, in a partial negative judgment S not distributed but Р distributed.

25. COMPLEX CONNECTIVE JUDGMENTS

A complex proposition is one that consists of several simple ones connected by logical connectives.. The following types of complex judgments are distinguished:

1) connecting, 2) dividing, 3) conditional, 4) equivalent. The truth of such complex judgments is determined by the truth of their simple constituents.

Connective (conjunctive) judgments

A connective, or conjunctive, is a proposition consisting of several simple ones connected by the logical connective “and”. For example, the proposition “Theft and fraud are intentional crimes” is a connecting proposition consisting of two simple ones: “Theft is an intentional crime,” “Fraud is an intentional crime.” If the first is denoted р, and the second - q, then the connecting proposition can be expressed symbolically as р ∧

qWhere р и q - members of the conjunction (or conjuncts), ∧ - symbol of the conjunction.

In natural language, the conjunctive connective can also be represented by such expressions as "a", "but", "as well", "like", "although", "however", "despite", "at the same time", etc. For example, "When the court determines the amount of damages to be compensated, not only the damages (R), but also the specific situation in which the losses were caused (Q), as well as the financial situation of the employee (r)". Symbolically this judgment can be expressed as follows: р ∧

q ∧ r.

A connecting proposition can be expressed in one of three structures.

Two subjects and one predicate (S' and S″ are Р).

For example, "Confiscation of property and deprivation of title are additional criminal sanctions."

One subject and two predicates (S is P' and P″).

For example, "Crime is a socially dangerous and illegal act."

Two subjects and two predicates (S' and S″ are P´ and P″). For example, “Fundamental human rights and freedoms are inalienable and belong to everyone from birth.”

The truth of a connecting proposition is determined by the truth of its constituent simple propositions. A connecting proposition is true only if its simple parts are true. If at least one simple proposition is false, then the conjunction as a whole is also false.

26. CONDITIONAL (IMPLICATIVE) AND COMPLEX DIVISION (DISJUNCTIVE) JUDGMENTS

Conditional, or implicative, is a proposition consisting of two simple ones connected by the logical connective “if... then...”. For example: “If the fuse melts, the light bulb goes out.” The first judgment is “The fuse is melting” - antecedent (previous), second - "The electric lamp goes out" - consequent (subsequent). If the antecedent is designated р, consequent - q, and the connective “if... then...” is marked “→”, then the implicative judgment can be symbolically expressed as (p → q).

The implication is true in all cases except one: if the antecedent is true and the consequent is false, the implication will always be false. The combination of the true antecedent, e.g. "The fuse melts", and the false consequent - "The electric lamp does not go out" - is an indicator of the falsity of the implication.

In natural language, to express conditional propositions, not only the conjunction “if... then...” is used, but also “there... where”, “then... when...”, “to the extent... since. ..”, etc. Grammatical indicators of implication can be, in addition to the conjunction “if... then...”, such phrases as “if there is... it follows”, “in case... it follows... ", "provided... comes...", etc. At the same time, legal implications can be constructed in the law and other texts without special grammatical indicators. For example: “Secret theft of someone else’s property (theft) is punishable...” or “Knowingly false denunciation of a crime is punishable...”, etc. Each of these instructions has an implicative formula: “If a certain illegal act is committed, then it is followed by legal sanction."

A disjunctive, or disjunctive, is a proposition consisting of several simple ones connected by the logical connective “or”. For example, the proposition “A purchase and sale agreement can be concluded orally or in writing” is a disjunctive proposition consisting of two simple ones: “A purchase and sale agreement can be concluded orally”; "The purchase and sale agreement may be concluded in writing." If the first one is designated р, and the second - q, then the disjunctive judgment can be expressed symbolically as р ∨

qWhere р и q - disjunction members (disjunctions), ∨ - disjunction symbol.

A disjunctive judgment can be either two- or multi-component: p ∨

q... ∨ n.

In a language, a disjunctive judgment can be expressed by one of three logical-grammatical structures.

Two subjects and one predicate (S' or S″ is R). For example, "Theft on a large scale or committed by a group of persons has an increased public danger."

One subject and two predicates (S is P´ or P″).

For example, "Theft is punishable by corrective labor or imprisonment."

Two subjects and two predicates (S´ or S″ is P' or P″). For example, “Exile or expulsion may be applied as a primary or additional sanction.”

27. TYPES OF DISJUNCTION

Non-strict and strict disjunction

Since the connective “or” is used in natural language in two meanings - connective-disjunctive and exclusive-disjunctive, two types of disjunctive judgments should be distinguished:

1) non-strict (weak) disjunction and 2) strict (strong) disjunction.

Nonstrict disjunction - a judgment in which the link "or" is used in a connecting-separating sense (symbol ∨). For example: "Cold weapons can be piercing or cutting" - symbolically р ∨

q. The connective “or” in this case separates, since such types of weapons exist separately, and connects, because there are weapons that simultaneously pierce and cut.

A non-strict disjunction will be true if at least one term of the disjunction is true and false if both of its terms are false.

Strict disjunction - a judgment in which the link "or" is used in a separating sense (symbol - double disjunction). For example: “An act can be intentional or careless,” symbolically

The terms of a strict disjunction, called alternatives, cannot be both true. If an act is committed intentionally, then it cannot be considered negligent, and, conversely, an act committed through negligence cannot be classified as intentional.

A strict disjunction will be true if one term is true and the other term is false; it will be false if both terms are true or both are false. Thus, a proposition of strict disjunction will be true if one alternative is true, and false if both alternatives are false and both are true.

The separating copula in the language is usually expressed using the unions "or", "or". In order to strengthen the disjunction to an alternative meaning, double conjunctions are often used: instead of the expression "p or q" they use "or p, or q", and together "p or q" - "either p or q". Since there are no unambiguous conjunctions for non-strict and strict division in grammar, the question of the type of disjunction in legal and other texts should be decided by a meaningful analysis of the corresponding judgments.

Complete and incomplete disjunction

Complete or closed is a disjunctive judgment that lists all the characteristics or all types of a certain kind.

Symbolically, this judgment can be written as follows: < p ∨

q ∨

r >. For example: “Forests are deciduous, coniferous or mixed.” The completeness of this division (in symbolic notation is indicated by the sign < ... >) is determined by the fact that there are no other types of forests in addition to those indicated.

Incomplete, or open, is a disjunctive judgment that does not list all the characteristics or not all types of a certain kind.. In symbolic notation, the incompleteness of a disjunction can be expressed by an ellipsis: р ∨

q ∨

r ∨ ... In natural language, the incompleteness of a disjunction is expressed by the words: “etc.,” “etc.,” “and the like,” “others,” etc.

28. EQUIVALENT JUDGMENTS. LOGICAL RELATIONSHIPS BETWEEN INCOMPATIBLE JUDGMENTS

Equivalent is a judgment that includes as components two judgments connected by a double (direct and inverse) conditional dependence, expressed by the logical connective “if and only if...

That...". For example: “If and only if a person has been awarded orders and medals (R), then he has the right to wear the appropriate order bars (q)".

The logical characteristic of this judgment is that the truth of the reward statement (R) is considered as a necessary and sufficient condition for the truth of the statement about the right to wear order bars (Q). In the same way, the truth of the statement about the existence of the right to wear order bars (Q) is a necessary and sufficient condition for the truth of the statement that the person was awarded the corresponding order or medal (R). Such mutual dependence can be symbolically expressed by the double implication p ↔ q, which reads: "If and only if рthen q". Equivalence is also expressed by another sign: р ≡

In natural language, including in legal texts, conjunctions are used to express equivalent judgments: “only provided that... then...”, “if and only if... then.. .", "only then... then...", etc.

Judgment р = q true when both propositions take on the same value, being either true or false at the same time. This means that the truth р enough to be true q, and vice versa. The relationship between them is also characterized as necessary, falsity р serves as an indicator of falsehood q, and falsity q points to falsehood р.

Logical relations between incompatible propositions.

Incompatible are propositions A and E, A and 0. E and I, which cannot be true at the same time. There are two types of incompatibility: opposition and contradiction.

1. Opposite (contrary) are propositions A and E, which cannot be true at the same time, but can be false at the same time.

The truth of one of the opposite judgments determines the falsity of the other: A → ⌉E; E → ⌉A. For example, the truth of the proposition "All officers are military personnel" determines the falsity of the proposition "No officer is a military personnel." If one of the opposite judgments is false, the other remains indefinite - it can be both true and false: ⌉A → (E ∨ ⌉E); ⌉E → (A ∨ ⌉A).

2. Contradictory (contradictory) propositions are propositions A and O, E and I, which at the same time cannot be either true or false.

A contradiction is characterized by strict, or alternative, incompatibility: if one of the judgments is true, the other will always be false; if the first is false, the second will be true. The relationship between such judgments is governed by the law of the excluded middle.

If A is recognized as true, then O will be false (A → ⌉O); when true, E will be false I: (E → ⌉I). And vice versa: if false, A will be true O (⌉A → O); and if false, E will be true I (⌉ E → I).

29. LOGICAL RELATIONS BETWEEN SIMPLE JUDGMENTS

Relations are established not between any, but only between comparable, i.e., judgments that have a general meaning.

Judgments that have different subjects or predicates are incomparable.. These are, for example, two propositions: “There are pilots among the astronauts”; "There are women among the astronauts."

Judgments with the same subjects and predicates and differing by a copula or quantifier are comparable.. For example: “All American Indians live on reservations”; "Some American Indians do not live on reservations."

Relationships between simple propositions are usually viewed using a mnemonic scheme called the logical square. Its peaks symbolize simple categorical judgments - A, E, I, O; sides and diagonals - the relationship between judgments.

Among comparable judgments, compatible and incompatible judgments are distinguished.

Compatible propositions are propositions that can be true at the same time.. There are three types of compatibility: equivalence (full compatibility), partial compatibility (subcontrary) and subordination.

1. Equivalent are those judgments that have the same logical characteristics: the same subjects and predicates, the same type - affirmative or negative - connective, the same quantitative characteristic expressed by the quantifier.

With the help of the logical square, the relations between simple equivalent propositions are not illustrated.

2. Partial compatibility is characteristic of judgments I and O, which can be true at the same time, but cannot be false at the same time.. If one of them is false, the other will be true: ⌉1→0,⌉0 → I. For example, if the proposition “Some grains are poisonous” is false, the proposition “Some grains are not poisonous” will be true. At the same time, if one of the particular judgments is true, the other can be either true or false: I → (O ∨ ⌉0); O → (I ∨ ⌉I).

3. Subordination takes place between judgments A and I, E and O. They are characterized by the following two dependencies.

When the general proposition is true, the particular proposition will always be true: A → I, E → O. For example, if the general proposition "Every legal relationship is governed by the rules of law" is true, the particular one will be true - "Some legal relations are regulated by the rules of law." If the proposition "No cooperative belongs to state organizations" is true, the proposition "Some cooperatives do not belong to state organizations" will also be true.

If the particular proposition is false, the general proposition will also be false: ⌉I → ⌉A; ⌉O → ⌉E.

Under subordination, the following dependencies remain undefined: when the general proposition is false, the subordinate particular can be either true or false: ⌉A → (I ∨⌉I); ⌉Е → (О ∨ ⌉О);

when the subordinate particular is true, the general can be either true or false: I → (А ∨ ⌉А); O → (E ∨⌉E).

30. LOGICAL RELATIONSHIPS BETWEEN COMPLEX JUDGMENTS

Compound judgments can be comparable or incomparable.

Incomparable - these are judgments that do not have common proportional variables. For example,

р ∧

q и m ∧ n.

Comparable - are propositions that have the same propositional variables (components) and differ in logical connectives, including negation. For example, the following two propositions are comparable: “Norway or Sweden have access to the Baltic Sea” (p ∨ q); “Neither Norway nor Sweden have access to the Baltic Sea” (⌉ р ∧ ⌉q).

Compound comparable judgments can be compatible or incompatible.

Comparable propositions are those that can be true at the same time. There are three types of compatibility of complex judgments: equivalence, partial compatibility and subordination.

1. Equivalent - these are judgments that take on the same values, that is, they are simultaneously either true or false.

The equivalence relation allows one to express some complex judgments through others - conjunction through disjunction or implication, and vice versa.

1. Expressing conjunction through disjunction: ⌉(A ∧

6) ≡ ⌉A ∨ ⌉B.

2. Expressing disjunction through conjunction: ⌉(A ∨

c) ≡ ⌉A ∧ ⌉B.

3. Expression of implication in terms of conjunction: A → B ≡ (A ∧ ⌉B)].

4. Expression of implication through disjunction: A → B ≡ ⌉A ∨ B].

2. Partial compatibility is characteristic of propositions that can be true at the same time, but cannot be false at the same time..

3. Subordination between judgments occurs in the case when, if the subordinate is true, the subordinate will always be true.

31. MODALITY OF JUDGMENTS. EPISTEMIC MODALITY

Judgment as a form of thinking contains two kinds of information - basic and additional. Basic information finds explicit expression in the subject and predicate of the judgment, in the logical connective and quantifiers. Additional information refers to the characteristics of the logical or actual status of the judgment, to its evaluative and other characteristics. Such information is called modality of judgment. It may be expressed in separate words, or it may not have an explicit expression. In this case, it is revealed by analyzing the context.

Modality - this is additional information explicitly or implicitly expressed in a judgment about the degree of its validity, logical or factual status, about its regulatory, evaluative and other characteristics.

epistemic (from the Greek episteme - the highest type of reliable knowledge) modality - this is information expressed in a judgment about the grounds for its acceptance and the degree of validity. These foundations include faith and knowledge.

According to the epistemic status, faith is a spontaneous, uncritical acceptance of other people's opinions, true or false, progressive or reactionary.

Knowledge as a logical justification is the acceptance of a judgment as true or false due to its validity by other judgments, from which the accepted judgment logically follows as a consequence.

According to the degree of validity among knowledge, two non-overlapping classes of judgments are distinguished: reliable and problematic.

1. Reliable judgments are sufficiently justified true or false judgments.

Their truth or falsity is established either by direct verification, or indirectly, when the judgment is confirmed by empirical or theoretical positions.

Reliability refers to such a modal characteristic of judgment, which, like the concepts of truth and falsehood, does not change in degrees. Two statements cannot be said to be "more certain" than the other. In the case of sufficient validity of the judgment, it is considered proven, thereby reliable, that is, true or false without change in degrees.

2. Problematic judgments are judgments that cannot be considered reliable due to their lack of validity. Since the truth or falsity of such judgments has not been precisely established, they only pretend to be so. Hence their names: problematic, plausible or probable.

In natural language, introductory words usually serve as indicators of the problematicness of a judgment: apparently, probably, it seems, perhaps, one can assume, etc.

In a forensic study, in the form of problematic judgments, versions (hypotheses) are built about the circumstances of the cases under investigation. Being justified, plausible judgments direct the investigation in the right direction and contribute to the establishment of reliable results in each case.

The validity of problematic judgments can be represented in terms of probability theory.

The logical probability of a judgment in this case means the degree of its validity.

32. DEONTIC MODALITY

Deontic (from Greek - duty) modality - it is a request, advice, order or instruction expressed in a judgment that encourages someone to take specific actions.

Among the prescriptions, it is necessary to single out normative prescriptions, including the rules of law.

Among the rules of law there are:

1) law-binding, 2) law-prohibiting and 3) law-granting.

1. Legally binding norms are formulated using the words: obligated, must, must, recognized, etc.. Thus, one of the procedural requirements states: “The preliminary investigation in criminal cases must be completed no later than within two months.” An example from civil law: “The organization is obliged to compensate for damage caused due to the fault of its employees in the performance of their labor (official) duties.”

Grammatically, legal obligation can also be expressed in the form of a statement, for example: "The prosecutor oversees the legality of initiating a criminal case." In this case, the duty of the prosecutor to exercise supervision is meant. In the same way: "The verdict is passed in the name of the Russian Federation" - should be understood as an obligation and obligation, and not as a statement of fact.

2. Prohibitory norms are formulated using the words: prohibited, not entitled, cannot, not allowed, etc.. For example: “It is prohibited to solicit testimony from the accused through violence, threats and other illegal measures.” Criminal proceedings provide: “No one may be arrested except by order of the court or the sanction of the prosecutor.” 3.

Law-providing norms are formulated using the words: has the right, can have, can apply, etc..

For example: "The tenant of the residential premises has the right to terminate the contract at any time." Another rule reads: "A person who has handed over things for storage has the right to demand them back at any time." The criminal law prescribes: "Any citizens who are not interested in the case can be called as witnesses," etc.

Obligation and prohibition can be expressed through each other: the obligation to perform a certain action is equivalent to the prohibition not to perform it.

A rationally constructed legal and regulatory system must satisfy the minimum modal deontic requirements:

1) consistency;

2) balance;

3) completeness.

33. ALETIC MODALITY

Alethic (from Greek - true) modality - this is information expressed in a judgment in terms of necessity-randomness or possibility-impossibility about the logical or factual determinacy (conditionality) of the judgment.

The judgments with which we operate are accepted as logically significant, that is, as true or false, not arbitrarily, but for certain reasons. Such grounds for the adoption of judgments are either the structural and logical characteristics of the judgments themselves, or their relationship with the actual state of affairs in reality. Two ways of conditionality, or determinism, of judgments predetermine the corresponding types of modalities.

Logical modality - this is the logical determinacy of a judgment, the truth or falsity of which is determined by the structure, or form, of the judgment.

To logically true, for example, include judgments expressing the laws of logic; to logically false - internally contradictory judgments. All other judgments, the truth or falsity of which cannot be determined on the basis of their structure, constitute the class of factually determined judgments.

Factual modality is associated with the objective, or physical, determination of judgments, when their truth and falsity are determined by the state of affairs in reality. Judgments in which the connection between terms corresponds to real relationships between objects are considered factually true. An example of such a proposition: “The Eiffel Tower is located in Paris.” Factually false are judgments in which the relationship between terms does not correspond to reality. For example: “No mammal lives in water.”

In fact, judgments that contain information about the laws of science are necessary.. In natural language, such judgments are often expressed using the words “necessary”, “obligatory”, “certainly”, etc.

In fact, random are judgments that do not contain information about the laws of science, and their truth and falsity are determined by specific empirical conditions. For example, the judgment “Napoleon died on May 5, 1821” is actually accidental, since Napoleon’s death could have occurred either before or after this date.

In fact, judgments containing information about the fundamental compatibility of phenomena expressed in the subject and predicate are possible.. For example: “There may be an earthquake in South America this year” or another proposition: “Football team A can win the match against team B.” This means that in both cases, opposite outcomes cannot be ruled out - there may not be an earthquake in South America this year; Team A may not win the match against Team B.

In natural language, words are indicators of possibility judgments: perhaps, perhaps, not excluded, others are allowed when they are used as predicates (and not introductory words).

34. LOGICAL CHARACTERISTICS OF QUESTIONS

Question - this is a thought expressed in an interrogative sentence, aimed at clarifying or supplementing the initial, or basic, knowledge. In the process of cognition, any question is based on some initial knowledge, which acts as its basis, acting as a prerequisite for the question. The cognitive function of the question is realized in the form of an answer to the question posed.

In legal proceedings, the question-answer form serves as a procedural and legal algorithm that determines the main directions, the most important positions and the limits of judicial research in criminal and civil cases.

Depending on the quality of the basic knowledge contained in the question, there are:

1) correctly placed, or correct - a question, the premise of which is true consistent knowledge;

2) misplaced or incorrect - a question with a false or inconsistent basis. An example would be the following question: "What kind of energy is used on a UFO?".

According to the cognitive function, questions are divided into two main types:

1) A clarifying question is a question aimed at identifying the truth of the judgment expressed in it.. For example: “Is it true that Columbus discovered America?” A grammatical feature of clarifying questions is the presence of the particle whether in the sentence: “Is it true that...”; "Does it..."; “Is it really that...” - and other synonymous expressions;

2) a replenishing question is a question aimed at clarifying new properties of the phenomena under study.

The grammatical feature of complementary questions is the presence of interrogative words in the sentence: who? What? When? How? - and others, with the help of which they seek to obtain additional information about what the object under study is.

By their composition, whether-questions and what-questions can be simple or complex.

A simple question is one that does not include other questions as components.. All of the above examples of whether-questions and what-questions are simple.

A complex question is one that includes other questions as components, united by logical connectives.. Depending on the type of connection, difficult questions may be:

a) connective (conjunctive);

b) dividing (disjunctive);

c) mixed (connecting and separating).

Depending on the topic under discussion:

1) substantive question - this is a request, directly or indirectly related to the topic under discussion, the answer to which clarifies or supplements the original information;

2) off topic question is a question that is not directly related to the topic under discussion. Usually such questions seem to be only superficially related to the problem under discussion. Acceptance and discussion of such issues often leads the discussion away from the main idea.

35. LOGICAL CHARACTERISTICS OF ANSWERS

Response - a new judgment that clarifies or supplements the initial knowledge in accordance with the question posed. Finding an answer involves turning to a specific area of theoretical or empirical knowledge, which is called the area of search for answers. The knowledge obtained in the answer, expanding or clarifying the initial information, can serve as the basis for raising new, deeper questions about the subject of research.

Among the answers are distinguished: true and false; direct and indirect; short and extended; complete and incomplete; exact (definite) and inexact (indefinite).

1. True and false answers differ in relation to reality.

2. Direct and indirect differ in the scope of the search.

A direct answer is an answer taken directly from the area of search for answers, the construction of which does not involve additional information and reasoning.. For example, a direct answer to the question “In what year did the Russo-Japanese War end?” there will be a judgment: “The Russo-Japanese War ended in 1904.” A direct answer to the question "Is a whale a fish?" there will be a judgment: “No, the whale is not a fish.”

An answer is called indirect, which is received from a wider area than the area of search for the answer, and from which the necessary information can be obtained only by inference. So, for the question “In what year did the Russo-Japanese War end?” the following answer will be indirect: “The Russo-Japanese War ended one year before the First Russian Revolution.” To the question "Is a whale a fish?" the indirect answer would be: “The whale is a mammal.”

3. Short and long answers differ in grammatical form.

Brief ones are monosyllabic affirmative or negative answers: “yes” or “no”.

Expanded answers are answers, each of which repeats all the elements of the question.. For example, to the question “Was J. Kennedy a Catholic?” affirmative answers can be received: short - “Yes”; expanded - “Yes, J. Kennedy was a Catholic.” Negative answers will be as follows: short - “No”; expanded - “No, J. Kennedy was not a Catholic.”

4. Complete and incomplete responses differ in the amount of information provided in the response..

5. Accurate (definite) and inaccurate (vague) answers differ in their correspondence to the characteristics of the question. Inaccurate answers are expressed in the ambiguous use of concepts and question words.

Ambiguous terms are often used in catchy or "provocative" questions that contain hidden information.

Uncertainty in the answers may be the result of the ambiguity of the concepts used in the formulation of the question.

The accuracy of the answer to the what-question depends on the degree of certainty of the question words: who? What? When? How? etc., which in themselves, without taking into account the situation and context, are not distinguished by sufficient certainty.

36. CONCLUSION AS A FORM OF THINKING. TYPES OF CONCLUSIONS

Inference - is a form of thinking by which a new judgment is derived from one or more judgments.

Any conclusion consists of premises, conclusion and conclusion.

The premises of an inference are the initial judgments from which a new judgment is derived. A conclusion is a new judgment obtained logically from the premises. The logical transition from premises to conclusion is called inference.

For example: "The judge cannot participate in the consideration of the case if he is the victim (1). Judge N. is the victim (2). Therefore, he cannot participate in the consideration of the case (3)."

In this conclusion, the 1st and 2nd judgments are premises, the 3rd judgment is the conclusion.

When analyzing the conclusion, it is customary to write the premises and the conclusion separately, placing them under each other. The conclusion is written under the horizontal line separating it from the premises and denoting the logical consequence. The words "therefore" and close to it in meaning ("means", "therefore", etc.) are usually not written under the line. Accordingly, the given example will take the following form:

A judge cannot participate in the consideration of a case if he is a victim.

Judge N. - victim.

__________________________

Judge N. cannot participate in the consideration of the case.

The relationship of logical consequence between the premises and the conclusion presupposes a connection between the premises in terms of content. If the judgments are not related in content, then the conclusion from them is impossible. If there is a meaningful connection between the premises, we can obtain new true knowledge in the process of reasoning, subject to two conditions: first, the initial judgments - the premises of the conclusion must be true; secondly, in the process of reasoning, one should follow the rules of inference, which determine the logical correctness of the conclusion.

Inferences are divided into the following types.

1. Depending on the severity of the inference rules, there are demonstrative (necessary) and non-demonstrative (plausible) conclusions.

Demonstrative inferences are characterized by the fact that the conclusion in them necessarily follows from the premises, i.e. the logical consequence in such conclusions is a logical law. In non-demonstrative inferences, the rules of inference provide only the probabilistic conclusion of the conclusion from the premises.

2. According to the nature of the connection between knowledge of varying degrees of generality, expressed in premises and conclusions, there are three types of inferences: deductive (from general knowledge to particular), inductive (from private to general knowledge), reasoning by analogy (from private knowledge to private).

37. DIRECT DEDUCTIVE CONCLUSIONS: TRANSFORMATION

deductive (from lat. - excretion) are called inferences in which the transition from general knowledge to specific knowledge is logically necessary.

Deductive inferences, depending on the number of premises, are divided into direct and indirect.

Direct inferences are those in which the conclusion is deduced from one premise, and mediated inferences are those in which the conclusion is deduced from two premises..

Immediate inferences include: transformation, inversion, opposition to a predicate, reasoning on a logical square.

The conclusions in each of these conclusions are obtained in accordance with the logical rules, which are determined by the type of judgment - its quantitative and qualitative characteristics.

Transformation

The transformation of a judgment into a judgment opposite in quality to a predicate that contradicts the predicate of the original judgment is called transformation. The transformation is based on the rule: double negation is equivalent to the statement ⌉(⌉ р) ≡ р.

It is possible to transform general affirmative, general negative, particular affirmative and particular negative judgments.

General affirmative judgment (BUT) turns into a negative (E). For example: “All employees of our team are qualified specialists. Therefore, not a single employee of our team is an unqualified specialist.”

All S are R.

No S is a non-R.

General negative judgment (E) turns into a universal affirmative (A). For example: “No religious teaching is scientific. Therefore, every religious teaching is unscientific.”

No S is R.

All S are non-R.

Partial affirmative judgment (I) turns into partial negative (O). Eg: "Some states are federal. Therefore, some states are not non-federal."

Some S are R.

Some S's are not non-P's.

A partial negative judgment (O) turns into a partial affirmative one (I). For example: "Some crimes are not intentional. Therefore, some crimes are unintentional."

Some S's are not R's.

Some S's are not-P's.

38. DIRECT DEDUCTIVE INCLUSION: APPEAL

A transformation of a proposition, as a result of which the subject of the original proposition becomes a predicate, and the predicate - the subject of imprisonment is called treatment.

The appeal obeys the rule: a term that is not distributed in the premise cannot be distributed in the conclusion.

Distinguish between simple (pure) handling and handling with restriction.

Simple, or pure, is called circulation without changing the amount of judgment. This is how judgments are addressed, both terms of which are distributed or both of which are not distributed. If the predicate of the initial judgment is not distributed, then it will not be distributed in the conclusion, where it becomes the subject. Therefore, its volume is limited. This type of reversal is called a constraint reversal.

General affirmative judgment (BUT) applies to a private 🇧🇷, i.e., with a constraint. For example: "All the students of our group (S) passed the exams (P). Therefore, some of the students who passed the exams (P) are students of our group (S)." In the original proposition, the predicate is not distributed, therefore, becoming the subject of the conclusion, it is also not distributed. Its scope is limited ("some passers").

All S are R.

Some P are S.

General affirmative highlighting judgments (the predicate is distributed in them) are addressed without restriction according to the scheme:

All S, and only S, are P. All P are S.

A general negative judgment (E) turns into a general negative (E), i.e. without limitation. For example: “Not a single student in our group (S) is a failure (P). Therefore, not a single student (P) is a student in our group (S).”

No S is P. No P is S.

Private affirmative judgment (I) turns into a private affirmative (I). This is a simple (pure) appeal. A predicate that is not distributed in the initial judgment is also not distributed in the conclusion. The amount of judgment does not change. For example: “Some students in our group (S) are excellent students (P). Therefore, some excellent students (P) are students in our group (S).

Some S are R.

Some P are S.

A particular affirmative distinguishing proposition (the predicate is distributed) turns into a general affirmative. For example: “Some socially dangerous acts (S) are crimes against justice (P). Consequently, all crimes against justice (P) are socially dangerous acts (S).”

Some S, and only S, are P.

All P are S.

Particularly negative judgments do not apply.

39. DIRECT DEDUCTIVE INCLUSION: OPPOSITION TO A PREDICT

Transformation of a judgment, as a result of which the subject becomes a concept that contradicts the predicate, and the predicate - the subject of the original judgment is called opposition to the predicate.

The opposition to the predicate can be regarded as the result of transformation and conversion: by transforming the original proposition S-P, we establish the relation of S to non-P; the proposition obtained by transformation is reversed, and as a result the relation of non-P to S is established.

The conclusion obtained by opposing the predicate depends on the quantity and quality of the original judgment.

A generally affirmative judgment (A) is transformed into a generally negative one (E). For example: “All lawyers have a legal education. Therefore, no one who does not have a legal education is a lawyer.”

All S are R.

No non-P is S.

A general negative judgment (E) is transformed into a particular affirmative one (I). For example: “Not a single industrial enterprise in our city is unprofitable. Consequently, some unprofitable enterprises are industrial enterprises in our city.”

No S is R.

Some non-Ps are S.

The particular affirmative judgment (I) is not transformed by opposition to the predicate.

A partial negative judgment (O) is transformed into a partial affirmative one (I). Eg: "Some witnesses are not adults. Therefore, some minors are witnesses."

Some S's are not R's.

Some non-Ps are S.

40. DIRECT DEDUCTIVE CONCLUSION: LOGICAL SQUARE CONVERSION. RELATIONS OF CONTRADICTIONS AND OPPOSITES

Given the properties of the relationship between the categorical propositions A, E, I, O, which are illustrated by the logical square scheme, one can draw conclusions by establishing the following of the truth or falsity of one judgment from the truth or falsity of another judgment.

The relation of contradiction (contradictority): A-O, E-I.

Since the relationship between contradictory judgments is subject to the law of the excluded middle, from the truth of one judgment follows the falsity of another judgment, from the falsity of one - the truth of the other. For example, from the truth of the universally affirmative proposition (A) "All peoples have the right to self-determination" follows the falsity of the particular-negative proposition (O) "Some peoples do not have the right to self-determination"; from the truth of the particular affirmative judgment (I) "Some court verdicts are acquittal" follows the falsity of the general negative judgment (E) "Not a single court verdict is acquittal."

Conclusions are built according to the schemes:

A → ⌉O; ⌉A → O; E →⌉I;⌉E → I.

Opposite (contrary) relationship: A-E. The truth of one proposition implies the falsity of another, but the falsity of one of them does not imply the truth of the other. For example, from the truth of the generally affirmative proposition (A) “All peoples have the right to self-determination,” the falsity of the generally negative proposition (E) “No people has the right to self-determination” follows. But from the falsity of proposition A, “All court verdicts are acquittal,” the truth of proposition E, “Not a single court verdict is acquittal,” does not follow. This proposition is also false.

Relations between opposite judgments obey the law of non-contradiction.

A → ⌉E, E→ ⌉A, ⌉A → (E ∨ ⌉E), ⌉E → (A ∨ ⌉A).

41. DIRECT DEDUCTIVE CONCLUSION: LOGICAL SQUARE CONVERSION. RELATIONSHIPS OF SUBCONTRARITY AND SUBMISSION

Relation of partial compatibility (subcontrast): I-O. The falsity of one proposition implies the truth of another, but the truth of one of them can entail both the truth and the falsity of another proposition. Both propositions can be true. For example, from the false proposition “Some doctors do not have a medical education” the true proposition “Some doctors have a medical education” follows; from the true proposition “Some witnesses have been interrogated” the proposition “Some witnesses have not been interrogated” follows, which can be either true or false.

Thus, subcontrarian judgments cannot be both false; at least one of them is true:

⌉I → O; ⌉0→I; I → (О ∨ ⌉О); O → (I ∨ ⌉1).

Subordination relationship (A-I, E-O). The truth of the subordinating judgment implies the truth of the subordinate judgment, but not vice versa: the truth of the subordinating judgment does not follow from the truth of the subordinate judgment; it can be true, but it can be false. For example, from the truth of the subordinate proposition A “All doctors have a medical education,” the truth of the subordinate proposition I “Some doctors have a medical education” follows. From a true subordinate proposition "Some witnesses have been examined" one cannot necessarily assert the truth of the subordinate proposition "All witnesses have been examined":

A → I; E → O; I → (A ∨ 1 A); O → (E ∨ 1E).

The falsity of the subordinate judgment follows from the falsity of the subordinate judgment, but not vice versa: from the falsity of the subordinate judgment the falsity of the subordinate does not necessarily follow; it may be true, but it may also be false. For example, from the falsity of the subordinate proposition (O) "Some peoples do not have the right to self-determination" follows the falsity of the subordinate proposition (E) "No people has the right to self-determination." If the subordinating proposition (A) "All witnesses have been examined" is false, then the subordinate proposition (I) "Some witnesses have been examined" may be true, but it may be false (it is possible that no witness has been examined).

In the logical square, the word "some" is used to mean "at least some."

⌉I →⌉ A; ⌉O → ⌉E; ⌉A → (I ∨ ⌉I); ⌉E→ (O ∨ ⌉0).

42. SIMPLE CATEGORICAL SYLLOGISM, ITS STRUCTURE AND AXIOM

A simple categorical syllogism consists of three categorical propositions, two of which are premises and the third is a conclusion. For example,

"The accused has the right to defense.

Gusev - accused.

Gusev has the right to protection."

Let us divide the judgments that make up the syllogism into concepts. There are three of these concepts, and each of them is part of two judgments: "Accused" - in the 1st (premise) as a subject and in the 2nd (premise) as a predicate; "has the right to protection" - in the 1st (premise) and in the 3rd (conclusion) as their predicates; "Gusev" - in the 2nd (premise) and in the 3rd (conclusion) as their subjects.

The concepts included in a syllogism are called syllogism terms. There are lesser, greater and middle terms.

The minor term of a syllogism is a concept that is the subject of the conclusion. (in our example, the concept of "Gusev").

The big term of a syllogism is a concept that in the conclusion is a predicate ("entitled to protection").

The smaller and larger terms are called extreme and are denoted respectively by the Latin letters S (smaller term) and P (larger term).

Each of the extreme terms is included not only in the conclusion, but also in one of the premises.

A premise that contains a minor term is called a minor premise, a premise that contains a larger term is called a major premise..

In our example, the first premise (1) will be the larger premise, and the second proposition (2) will be the smaller premise.

The middle term of a syllogism is a concept that is included in both premises and is absent in the conclusion. (in our example - "accused"). The middle term is denoted by the Latin letter M.

The accused (M) has the right to defense (P).

Gusev (S) - accused (M).

Gusev (S) is entitled to defense (P).

So, simple categorical syllogism - is an inference about the relationship of two extreme terms based on their relationship to the middle term.

Axiom of the syllogism substantiates the legitimacy of the conclusion, i.e., the logical transition from premises to conclusion: everything that is affirmed or denied regarding all objects of a certain class is affirmed or denied regarding each object and any part of the objects of this class.

In this example, everything that is asserted in relation to all the accused is also affirmed in relation to a specific accused.

43. RULES OF TERMS OF A SIMPLE CATEGORICAL SILLOGISM

From true premises, a true conclusion can be obtained only if the rules of the syllogism are observed. There are seven of these rules: three pertain to terms and four pertain to premises.

1st rule: a syllogism must have only three terms. The conclusion in a syllogism is based on the ratio of two extreme terms to the middle, so it cannot have less or more than three terms. Violation of this rule is associated with the identification of different concepts, which are taken as one and considered as a middle term. This error is based on a violation of the requirements of the law of identity and is called quadrupling terms. It is impossible, for example, to obtain a conclusion from the premises: “Laws are not created by people” and “A law is a normative act adopted by the highest body of state power,” because instead of three terms we are dealing with four: in the first premise we mean objective laws that exist independently of the consciousness of people, in the second - legal law established by the state. These are two different concepts that cannot be connected by extreme terms.

2st rule: the middle term must be distributed in at least one of the premises. If the middle term is not distributed in any of the premises, then the relationship between the extreme terms remains uncertain. For example, in the premises “Some lawyers (M) are members of the bar (P)”, “All employees of our team (S) are lawyers (M)” the middle term (M) is not distributed in the larger premise, since it is the subject of a private judgment, and is not distributed in a minor premise as a predicate of an affirmative judgment. Therefore, the middle term is not distributed in any of the premises. In this case, the necessary connection between the extreme terms (S and P) cannot be established.

3rd rule: a term not distributed in the premise cannot be distributed in the conclusion. Eg:

"Moral norms (M) are not sanctioned by the state (P).

Moral norms (M) - forms of social regulation (S).

Some forms of social regulation (S) are not sanctioned by the state (P).

The minor term (S) is undistributed in the premise (as the predicate of an affirmative proposition), so it is also undistributed in the conclusion (as the subject of a partial proposition). This rule prohibits making a conclusion with a distributed subject in the form of a general judgment ("No form of social regulation is sanctioned by the state"). The error associated with the violation of the rule of distribution of extreme terms is called illegal extension of a lesser (or greater) term.

44. RULES OF PREMISES OF A SIMPLE CATEGORICAL SILLOGISM

1st rule: at least one of the premises must be an affirmative proposition. From two negative premises the conclusion does not necessarily follow. For example, from the premises “Students of our institute (M) do not study biology (P)”, “Employees of the research institute (S) are not students of our institute (M)” it is impossible to obtain the necessary conclusion, since both extreme terms (S and P) are excluded from the average. Therefore, the middle term cannot establish a definite relationship between the extreme terms.

2st rule: if one of the parcels - negative judgment, then the conclusion must be negative. Eg:

A judge who is a relative of the victim (M) cannot participate in the case (P).

Judge K. (S) is a relative of the victim (M).

Judge K. (S) cannot participate in the case (P).

3st rule: at least one of the premises must be a general proposition. From two particular premises the conclusion does not necessarily follow. If both premises are partial affirmative propositions (II), then the conclusion cannot be drawn according to the 2nd rule of terms: in a particular affirmative proposition neither the subject nor the predicate are distributed, therefore the middle term is not distributed in any of the premises. If both premises are partial negative judgments (NP), then the conclusion cannot be drawn according to the 1st rule of premises. If one premise is partial affirmative and the other is partial negative (IO or 0I), then in such a syllogism only one term will be distributed - the predicate of the partial negative judgment. If this term is average, then a conclusion cannot be drawn, since according to the 2nd rule of premises, the conclusion must be negative. But in this case the predicate of the conclusion must be distributed, which contradicts the 3rd rule of terms:

1) the larger term, not distributed in the premise, will be distributed in the conclusion;

2) if the larger term is distributed, then the conclusion does not follow according to the 2nd rule of terms.

4rd rule: if one of the parcels - private judgment, then the conclusion must be private. If one premise is generally affirmative, and the other is particularly affirmative (AI, IA), then only one term is distributed in them - the subject of the generally affirmative judgment. According to the 2nd rule of terms, it must be a middle term. But in this case, the two extreme terms, including the smaller one, will not be distributed. Therefore, according to the 3rd rule of terms, the lesser term will not be distributed in the conclusion, which will be a private judgment. If one of the premises is affirmative and the other is negative, and one of them is particular (EI AO, OA), then two terms will be distributed: the subject and predicate of a general negative judgment (EI) or the subject of a general and the predicate of a particular judgment (AO, OA). But in both cases, according to the 2nd rule of premises, the conclusion will be negative, that is, a judgment with a distributed predicate. And since the second distributed term must be the middle one (2nd rule of terms), the smaller term will ultimately turn out to be undistributed, i.e. the conclusion will be partial.

45. FIRST FIGURE OF CATEGORICAL SYLLOGISM, ITS RULES, MODES AND ROLE IN COGNITION

In the premises of a simple categorical syllogism, the middle term can take the place of a subject or a predicate. Depending on this, four types of syllogism are distinguished, which are called figures.

Syllogism figures - these are its varieties, differing in the position of the middle term in the premises.

In the first figure, the middle term takes the place of the subject in the major and the place of the predicate in the minor premises.

The premises of a syllogism can be judgments that are different in quality and quantity: generally affirmative (A), generally negative (E), particular affirmative (/) and particular negative (O).

Varieties of syllogism that differ in the quantitative and qualitative characteristics of the premises are called modes of simple categorical syllogism. The total number of options in the four figures is 64 modes, but only 19 of them are correct, that is, corresponding to all the rules. According to the first figure, these are the modes: AAA, EAE, AII, EIO.

In addition to the general rules, there are special rules for figures.

Rules of the 1st figure:

1. Big premise - general judgment.

2. Minor premise - affirmative judgment. The first figure is the most typical form of deductive reasoning. From the general position, which often expresses the law of science, the legal norm, a conclusion is made about a separate fact, an isolated case, a specific person. This figure is widely used in judicial practice. The legal assessment (qualification) of legal phenomena, the application of the rule of law to a particular case, the imposition of punishment for a crime committed by a specific person, and other judicial decisions take the logical form of the 1st figure of the syllogism.

46. THE SECOND AND THIRD FIGURES OF THE CATEGORICAL SYLLOGISM, THEIR RULES, MODES AND ROLE IN COGNITION

In the second figure - the place of the predicate in both premises

Varieties of syllogism that differ in the quantitative and qualitative characteristics of the premises are called modes of simple categorical syllogism. The total number of options in the four figures is 64 modes, but only 19 of them for the second figure are correct, i.e., corresponding to all the rules: EAE, AEE, EIO, AOO.

In addition to the general rules, there are special rules for figures.

Rules of the 2st figure:

1. Big premise - general judgment.

2. One of the premises is a negative judgment.

The 2nd figure is used when it is necessary to show that a particular case (a specific person, fact, phenomenon) cannot be brought under a general position. This case is excluded from the list of things mentioned in the major premise. In judicial practice, the 2nd figure is used to conclude that there is no corpus delicti in this particular case, to refute provisions that contradict what is said in the premise expressing the general position.

In the third figure - the place of the subject in both premises

The premises of a syllogism can be judgments that are different in quality and quantity: generally affirmative (A), generally negative (E), particular affirmative (/) and particular negative (O).

According to the third figure, the following modes are correct: AAI, IAI, AII, EAO, OAO, EIO.

Rules of the 3st figure:

1. Minor premise - affirmative judgment.

2. Conclusion - private judgment.

Giving only private conclusions, the 3rd figure is used most often to establish the partial compatibility of features related to the same subject. In the practice of reasoning, the 3rd figure is used relatively rarely.

47. PURE CONDITIONAL CONCLUSION

A purely conditional inference is a conclusion in which both premises are conditional propositions.. Eg:

If the invention was created by the joint creative work of several citizens (p), all of them are recognized as co-authors of the invention (q). If they are recognized as co-authors of the invention (r), then the procedure for using the rights to an invention created in co-authorship is determined by the agreement between co-authors (r). If an invention was created by the joint creative work of several citizens (p), then the procedure for using the rights to an invention created in co-authorship is determined by an agreement between the co-authors (r).

In the above example, both premises are conditional propositions, and the consequence of the first premise is the basis of the second (q), from which, in turn, some consequence (r) follows. The common part of the two premises (q) allows us to connect the base of the first (p) and the consequence of the second (r). Therefore, the conclusion is also expressed in the form of a conditional proposition.

Schematic of purely conditional inference:

(p → q) ∧ (q → r),

(P → r).

The conclusion in purely conditional inference is based on the rule: the consequence of the effect is the consequence of the reason.

An inference in which the conclusion is obtained from two conditional premises is simple.

However, the conclusion may follow from a larger number of premises that form a chain of conditional propositions. Such inferences are called complex.

48. CONDITIONAL-CATEGORICAL CONCLUSION

Conditionally categorical is a conclusion in which one of the premises - conditional, and another premise and conclusion - categorical judgments.

This inference has two correct modes: affirmative and negative.

1. In affirmative mode (modus ponens) the premise, expressed by a categorical judgment, asserts the truth of the basis of the conditional premise, and the conclusion asserts the truth of the consequence; reasoning is directed from the assertion of the truth of the foundation to the assertion of the truth of the consequence. For example:

If the claim is brought by an incompetent person (p), then the court leaves the claim without consideration (q).

Claim brought by incompetent person (R). The court leaves the claim without consideration (q).

The first premise is a conditional proposition expressing the connection between the base (p) and the consequence (q). The second premise is a categorical judgment, which affirms the truth of the ground (p): the claim was brought by an incompetent person. Recognizing the truth of the ground (p), we recognize the truth of the consequence (q): the court leaves the claim without consideration.

The affirmative mode gives reliable conclusions. It has a schema:

2. In negating mode (modus tollens) the premise expressed by the categorical proposition denies

the truth of the consequence of the conditional premise, and the conclusion denies the truth of the foundation. Reasoning is directed from the denial of the truth of the consequence to the denial of the truth of the foundation. For example: If a claim is brought by an incapacitated person (p), then the court leaves the claim without consideration (q). The court did not leave the claim without consideration (⌉ q). It is not true that the suit was brought by an incompetent person (⌉p). Diagram of the negating mode:

It is easy to establish that two more varieties of conditionally categorical syllogism are possible: from the denial of the truth of the foundation to the denial of the truth of the consequence, and from the affirmation of the truth of the consequence to the affirmation of the truth of the foundation.

However, the conclusion on these modes will not be reliable. Thus, out of the four modes of conditionally categorical reasoning, which exhaust all possible combinations of premises, only two give reliable conclusions: affirming and denying. They express the laws of logic and are called the correct modes of a conditionally categorical inference. These mods obey the rule: the affirmation of the basis leads to the statement of the consequence and the negation of the consequence leads to the negation of the basis. The other two modes do not provide reliable conclusions. They are called irregular modes and obey the rule: negation of the reason does not necessarily lead to the negation of the consequence, and affirmation of the consequence does not necessarily lead to the affirmation of the reason.

49. DIVISION-CATEGORICAL CONCLUSION

An inference is called separative-categorical., in which one of the premises is divisive, and the other premise and conclusion are categorical judgments.

Simple judgments that make up a disjunctive (disjunctive) judgment are called members of the disjunction, or disjuncts. For example, the disjunctive proposition "Bonds may be bearer or registered" consists of two judgments - disjuncts: "Bonds may be bearer" and "Bonds may be registered", connected by the logical conjunction "or".

While affirming one term of the disjunction, we must necessarily deny the other, and, denying one of them, affirm the other. In accordance with this, two modes of divisive-categorical reasoning are distinguished: affirmative-denying and denying-asserting.

1. In affirmative-denying mode (modus ponendo tollens) the minor premise, the categorical proposition, affirms one term of the disjunction, the conclusion - also a categorical proposition - denies the other term. For example: Bonds can be bearer (p) or registered (q).

This bond is bearer (p). This bond is not registered (q).

Scheme of affirmative-denying mode:

where - symbol of strict disjunction.

A conclusion according to this mode is always valid if the rule is observed: the major premise must be an exclusive disjunctive judgment, or a judgment of strict disjunction. If this rule is not observed, a reliable conclusion cannot be obtained.

2. In denying-affirming mode (modus tollendo ponens) the minor premise denies one disjunct, the conclusion affirms another. For example: Bonds can be bearer (p) or registered (q). This bond is non-bearer (⌉p). This bond is registered (q).

Scheme of the denying-affirming mode:

where < > is a closed disjunction symbol.

An affirmative conclusion is obtained through negation: by denying one disjunct, we affirm another.

A conclusion according to this modus is always reliable if the rule is observed: in the major premise, all possible judgments - disjuncts must be listed, in other words, the major premise must be a complete (closed) disjunctive statement. Using an incomplete (open) disjunctive statement, a reliable conclusion cannot be obtained.

The separating premise may include not two, but three or more members of the disjunction.

50. CONDITIONAL DIVISION CONCLUSION

An inference in which one premise is conditional and the other - separative judgment, is called conditional-separative, or lemmatic (from lat. - assumption).

A disjunctive judgment can contain two, three or more alternatives, so lemmatic reasoning is divided into dilemmas (two alternatives), trilemmas (three alternatives), etc.

В simple design dilemma the conditional premise contains two grounds from which the same consequence follows. The dividing premise affirms both possible grounds, the conclusion affirms the consequence. The reasoning is directed from the assertion of the truth of the grounds to the assertion of the truth of the consequence:

If the accused is guilty of knowingly illegal detention (p), then he is subject to criminal liability for a crime against justice (r); if he is guilty of knowingly unlawful detention (q), then he is also subject to criminal liability for a crime against justice (r). The accused is guilty of either knowingly unlawful detention (p) or knowingly unlawful detention (q).

The accused is subject to criminal liability for a crime against justice (r).

В difficult design dilemma the conditional premise contains two bases and two consequences.

The separating premise asserts both possible consequences. The reasoning is directed from the assertion of the truth of the grounds to the assertion of the truth of the consequences:

The certificate can be bearer (p) or registered (r).

В simple destructive dilemma the conditional premise contains one basis, from which two possible consequences follow. The dividing premise denies both consequences, the conclusion denies the reason. The reasoning is directed from the denial of the truth of the consequences to the denial of the truth of the foundation.

If N. committed an intentional crime (p), then there was direct (q) or indirect intent (r) in his actions.

But there was neither direct (q) nor indirect intent (r) in N.'s actions.

The crime committed by N. is not intentional (r).

В complex destructive dilemma the conditional premise contains two bases and two consequences. The dividing premise denies both consequences, the conclusion denies both grounds. The reasoning is directed from the denial of the truth of the consequences to the denial of the truth of the grounds:

51. abbreviated syllogism (entimeme)

A syllogism with a missing premise or conclusion is called an abbreviated syllogism or enthymeme. (from Greek - in the mind).

The enthymemes of a simple categorical syllogism are widely used, especially inferences from the first figure. For example: "N. committed a crime and therefore is subject to criminal liability." A big premise is missing here: "A person who has committed a crime is subject to criminal liability." It is a public position.

A complete syllogism is built on the 1st figure:

The person who committed the crime (M) is subject to criminal liability (P).

N. (S) committed a crime (M).

H. (S) is subject to criminal liability (P).

Not only a larger, but also a smaller premise can be missed, as well as the conclusion: "The person who committed the crime is subject to criminal liability, which means that N. is subject to criminal liability." Or: "The person who committed the crime is subject to criminal liability, and N. committed the crime." The omitted parts of the syllogism are implied.

Depending on which part of the syllogism is missing, there are three types of enthymeme: with a missing major premise, with a missing minor premise, and with a missing conclusion.

An inference in the form of an enthymeme can also be constructed according to the 2nd figure; according to the 3rd figure, it is rarely built.

The form of an enthymeme is also taken by inferences, the premises of which are conditional and disjunctive judgments.

A conditionally categorical syllogism with a missing major premise: "A criminal case cannot be initiated, since the event of the crime did not take place." A big premise is missing here - the conditional proposition "If the event of the crime did not take place, then a criminal case cannot be initiated." It contains a well-known provision of the Criminal Procedure Code of the Russian Federation, which is implied.

Separating-categorical syllogism with the omitted major premise: "In this case, an acquittal cannot be passed, it must be guilty."

The big premise - the divisive judgment "In this case, either an acquittal or a guilty verdict can be passed" is not formulated.

Dividing-categorical syllogism with an omitted conclusion: "Death occurred either as a result of murder, or as a result of suicide, or as a result of an accident, or due to natural causes. Death occurred as a result of an accident."

A conclusion that denies all other alternatives is usually not formulated.

The use of abbreviated syllogisms is due to the fact that the missing premise or conclusion either contains a well-known provision that does not need oral or written expression, or it is easily implied in the context of the expressed parts of the conclusion. That is why reasoning proceeds, as a rule, in the form of enthymemes. But since not all parts of the conclusion are expressed in the enthymeme, the error lurking in it is more difficult to detect than in the full conclusion. Therefore, to check the correctness of the reasoning, it is necessary to find the missing parts of the conclusion and restore the enthymeme to a complete syllogism.

52. INDUCTIVE CONCLUSION, ITS TYPES AND LOGICAL STRUCTURE

The logical transition from knowledge about individual phenomena to general knowledge takes place in the form of inductive reasoning, or induction (from Latin - guidance).

Inductive inference is an inference in which, based on the attribute’s belonging to individual objects or parts of a certain class, a conclusion is drawn about its belonging to the class as a whole..

In the history of physics, for example, it has been experimentally established that iron rods conduct electricity well. The same property was found in copper rods and silver. Considering that these conductors belong to metals, an inductive generalization was made that electrical conductivity is inherent in all metals.

The premises of the inductive inference are judgments in which the information obtained empirically about the frequency of the feature P for a number of phenomena - S1, S2, Sn, belonging to the same class K. is fixed. The scheme of the inference has the following form:

1) S1 has a sign P;

S2 has a sign P;

................................

Sn has the sign R.

2) S1, S2.....Sn - elements (parts) of class K.

All objects of class K have the attribute R.

At the heart of the logical transition from premises to conclusions in inductive inference is the position, confirmed by millennia of practice, about the natural development of the world, the universal nature of the causal relationship, the manifestation of the necessary signs of phenomena through their universality and stable recurrence. It is these methodological provisions that justify the logical consistency and effectiveness of inductive conclusions.

The main function of inductive inferences in the process of cognition is generalization, that is, obtaining general judgments. In terms of their content and cognitive significance, these generalizations can be of a different nature - from the simplest generalizations of everyday practice to empirical generalizations in science or universal judgments expressing universal laws.

An important place belongs to inductive conclusions in forensic and investigative practice - on their basis, numerous generalizations are formulated regarding ordinary relations between people, motives and goals for committing unlawful acts, methods of committing crimes, typical reactions of perpetrators of a crime to the actions of investigating authorities, etc.

Depending on the completeness and completeness of the empirical study, two types of inductive reasoning are distinguished: complete induction and incomplete. In incomplete induction, popular and scientific are distinguished, depending on the method of selecting the source material. Scientific induction is divided, depending on the method of research, into induction by selection and induction by exclusion.

53. COMPLETE INDUCTION AND ITS ROLE IN COGNITION

Full induction - this is an inference in which, based on the membership of each element or each part of the class of a certain feature, a conclusion is drawn about its membership in the class as a whole.

Inductive reasoning of this kind applies only when dealing with closed classes, the number of elements in which is finite and easily observable. For example, the number of states in Europe, the number of industrial enterprises in a given region, the number of federal subjects in a given state, etc.

Let's imagine that the audit commission is tasked with checking the state of financial discipline in the branches of a particular banking association. It is known to have five separate branches. The usual way to check in such cases is to analyze the activities of each of the five banks. If it turns out that no financial violations were found in any of them, then a general conclusion can be made: all branches of the banking association observe financial discipline.

The scheme of inference of full induction has the following form:

1) S1 has a sign P;

S2 has a sign P;

................................

Sn has the sign R.

2) S1, S2.....Sn - constitute class K.

All objects of class K have the attribute R.

The information expressed in the premises of this inference about each element or each part of the class serves as an indicator of the completeness of the study and a sufficient basis for the logical transfer of the attribute to the entire class. Thus, the conclusion in the conclusion of complete induction is demonstrative. This means that if the premises are true, the conclusion will necessarily be true.

The cognitive role of the conclusion of complete induction is manifested in the formation of new knowledge about a class or kind of phenomena. The logical transfer of a feature from individual objects to the class as a whole is not a simple summation. Knowledge about a class or genus is a generalization, which is a new step in comparison with single premises.

In forensic research, demonstrative reasoning in the form of full induction with negative conclusions is often used. For example, an exhaustive enumeration of varieties excludes a certain method of committing a crime, the method of penetration of an attacker to the scene of a crime, the type of weapon with which the wound was inflicted, etc.

The applicability of complete induction in reasoning is determined by the practical enumerability of a set of phenomena. If it is impossible to cover the entire class of objects, then the generalization is built in the form of an incomplete induction.

54. INCOMPLETE INDUCTION AND ITS TYPES

Incomplete induction - this is an inference in which, based on the attribute belonging to some elements or parts of a class, a conclusion is made about its belonging to the class as a whole.

1) S1 has a sign P;

S2 has a sign P;

................................

Sn has the sign R.

2) S1, S2.....Sn belong to class K.

Class K, apparently, is characterized by the characteristic R.

The incompleteness of the inductive generalization is expressed in the fact that not all, but only some elements or parts of the class are investigated - from S1 to Sn. The logical transition in incomplete induction from some to all elements or parts of a class is not arbitrary. It is justified by empirical grounds - an objective relationship between the universal character of signs and their stable repetition in experience for a certain kind of phenomena. Hence the widespread use of incomplete induction in practice. So, for example, during harvesting, we conclude about the weediness, moisture content and other characteristics of a large batch of grain on the basis of individual samples. In production conditions, according to selective samples, they conclude about the quality of a particular mass product.

The inductive transition from some to all cannot claim to be a logical necessity, since the recurrence of a feature may be the result of a simple coincidence.

Thus, incomplete induction is characterized by a weakened logical consequence - true premises provide not a reliable, but only a problematic conclusion. At the same time, the discovery of at least one case that contradicts the generalization makes the inductive conclusion untenable.

On this basis, incomplete induction is referred to as plausible (non-demonstrative) inferences. In such conclusions, the conclusion follows from the true premises with a certain degree of probability, which can range from unlikely to very plausible.

A significant influence on the nature of logical consequence in the conclusions of incomplete induction is exerted by the method of selecting the source material, which manifests itself in the methodical or systematic formation of the premises of inductive reasoning. According to the method of selection, two types of incomplete induction are distinguished: by enumeration, which is called popular induction, and by selection, which is called scientific induction.

55. POPULAR INDUCTION

Popular induction (induction through simple enumeration) is a generalization in which, by means of enumeration, it is established that a characteristic belongs to certain objects or parts of a class and, on this basis, it is problematic to conclude that it belongs to the entire class.

In the process of investigating crimes, empirical inductive generalizations are often used regarding the behavior of persons involved in the crime. For example: persons who have committed crimes seek to hide from the court and investigation; Threats to kill are often carried out. Such empirical generalizations, or factual presumptions, often provide invaluable assistance to the investigation, despite the fact that they are problematic judgments.

Popular induction defines the first steps in the development of scientific knowledge. Any science begins with empirical research - observation of the relevant objects in order to describe them, classify them, identify stable connections, relationships and dependencies. The first generalizations in science are due to the simplest inductive conclusions through a simple enumeration of recurring features. They perform an important heuristic function of initial assumptions, conjectures and hypothetical explanations that need further verification and clarification.

In conditions where only some representatives of the class are studied, the possibility of an erroneous generalization is not excluded.

Erroneous conclusions about the conclusions of the popular induction may appear due to non-observance

requirements to take into account conflicting cases, which make the generalization untenable. This happens in the process of preliminary investigation, when the problem of the relevance of evidence is being solved, i.e., the selection from a multitude of factual circumstances only those that, in the opinion of the investigator, are relevant to the case. In this case, they are guided by only one, perhaps the most plausible or the most "close to the heart" version, and select only the circumstances confirming it. Other facts, and above all those that contradict the original version, are ignored. Often they are simply not seen and therefore not taken into account. Contradictory facts also remain out of sight due to insufficient culture, inattention, or defects in observation. In this case, the investigator is captured by the facts: out of the multitude of phenomena, he fixes only those that turn out to be predominant in the experience, and builds a hasty generalization on their basis. Under the influence of this illusion, further observations not only do not expect, but also do not admit the possibility of contradictory cases.

Erroneous inductive conclusions can appear not only as a result of delusion, but also as a result of unscrupulous, biased generalization, when contradictory cases are deliberately ignored or hidden. Such imaginary inductive generalizations are used as gimmicks.

Incorrectly constructed inductive generalizations often underlie various kinds of superstitions, ignorant beliefs and signs like the "evil eye", "good" and "bad" dreams, a black cat that crossed the road, etc.

56. SCIENTIFIC INDUCTION. INDUCTION BY SELECTION

Scientific induction is an inference in which a generalization is built by selecting the necessary and excluding random circumstances.

Depending on the methods of research, induction is distinguished by the method of selection (selection) and exclusion (elimination).

Induction by selection, or selective induction- this is an inference in which the conclusion about the belonging of a feature to a class (set) is based on knowledge about a sample (subset) obtained by methodically selecting phenomena from various parts of this class.

If in a popular generalization one proceeds from the assumption of a uniform distribution of the attribute P in the class K and thereby allows its transfer to K with simple repetition (Si, S2, Sn), then in scientific induction K is a non-uniform set with a non-uniform distribution of P in its various parts.

When forming a sample, one should diversify the conditions of observation. The selection of P from the various parts of K must take into account their specificity, weight and significance in order to ensure the representativeness, or representativeness, of the sample.

An example of induction by the selection method is the following discussion about a variety of winter wheat sown in one of the regions of Russia. So, when driving along a highway crossing one of the southern regions, it is noted along the way that in several regions (for example, in six) the fields are sown with the same variety of winter wheat. If, on this basis, one generalizes that the same variety is sown in all 25 districts, and therefore in the entire region, then it is obvious that such a popular induction will give an unlikely conclusion.

It is a different matter if the choice of the same number of districts is made not by chance, along the way, but taking into account differences in their location and climatic conditions. If the selected areas are southern and northern, inland and peripheral, steppe and forest-steppe, and at the same time the repeatability of the variety is established, then it can be assumed with a high probability that the entire region uses the same variety of winter wheat.

A reliable conclusion in this case is unlikely to be justified, since the possibility of using a different variety in areas that have not been directly observed is not excluded.

57. SCIENTIFIC INDUCTION. INDUCTION BY THE METHOD OF EXCLUSION

Scientific induction is an inference in which a generalization is built by selecting the necessary and excluding random circumstances.

Depending on the methods of research, induction is distinguished by the method of selection (selection) and exclusion (elimination).

Induction by exclusion, or eliminative induction- is a system of inferences in which conclusions about the causes of the phenomena under study are drawn by detecting confirming circumstances and excluding circumstances that do not satisfy the properties of a causal relationship.

The cognitive role of eliminative induction is the analysis of causal relationships. Causal is such a connection between two phenomena, when one of them, the cause, precedes and causes the other, the action. The most important properties of a causal connection, which predetermine the methodical nature of eliminative induction, are its following characteristics:

1. The universality of causality. There are no uncaused phenomena in the world.

2. Consistency in time. Cause always precedes action. In some cases, the action follows the cause instantly, in a matter of fractions of a second. For example, a shot from a firearm occurs as soon as the primer in the cartridge ignites. In other cases, the cause causes the action after a longer period of time. For example, poisoning can occur after a few seconds, minutes, hours or days, depending on

the strength of the poison and the state of the body. Since the cause always precedes the action, out of many circumstances in the process of inductive research, only those are selected that manifested themselves before the action of interest to us and exclude from consideration (eliminate) those that arose simultaneously with it and appeared after it. Sequence in time is a necessary condition for causation, but by itself it is not sufficient to discover the real cause. Recognition of this condition as sufficient often leads to an error called "after this, therefore, because of this" (post hoc, ergo propter hoc). Lightning, for example, was formerly considered the cause of thunder because sound is perceived later than a flash of light, although these are simultaneously occurring phenomena. In investigative practice, the threat of a certain person against another and the subsequent violence against the person of the second person are sometimes mistakenly interpreted as a causal connection, although it is well known that threats are not always carried out.

3. Causality is distinguished by the property of necessity. This means that an action can be carried out only in the presence of a cause, the absence of a cause necessarily leads to the absence of an action.

4. The unambiguous nature of the causal relationship. Each specific cause always causes a well-defined action corresponding to it. The relationship between cause and effect is such that changes in the cause necessarily entail changes in the effect, and vice versa, changes in the effect indicate a change in the cause.

58. METHOD OF SIMILARITY AS A METHOD OF SCIENTIFIC INDUCTION

Modern logic describes five methods for establishing causal relationships: the method of similarity, the method of difference, the combined method of similarity and difference, the method of concomitant changes, the method of residues.

similarity method

Using the similarity method, several cases are compared, in each of which the phenomenon under study occurs; Moreover, all cases are similar only in one way and different in all other circumstances.

The similarity method is called the method of finding the common in the different, since all cases are noticeably different from each other, except for one circumstance.

Consider an example of reasoning by the method of similarity. In the summer period, a medical center in one of the villages recorded three cases of dysentery in a short time (d). When clarifying the source of the disease, the main attention was paid to the following types of water and food, which more often than others can cause intestinal diseases in the summer: A - drinking water from wells; M - water from the river; B - milk; C - vegetables; F - fruits. The study showed that the spread of dysentery is associated, apparently, with the consumption of milk. This was later confirmed by additional studies.

The scheme of reasoning by the method of similarity has the following form:

1) ABC calls d;

2) MBF calls d;

3) MBC calls d. Apparently, B is the cause of d.

The similarity method yields high-likelihood conclusions if:

1) all possible causes of the phenomenon under study have been established;

2) it is established that circumstance B precedes event d;

3) all circumstances that are not necessary for the investigated action are excluded;

4) each of the circumstances does not interact with others.

Despite the problematic nature of the conclusion, the similarity method performs an important heuristic function in the process of cognition, it contributes to the construction of fruitful hypotheses, the verification of which leads to the discovery of new truths in science.

59. THE METHOD OF DIFFERENCE AS A METHOD OF SCIENTIFIC INDUCTION

According to the difference method, two cases are compared, in one of which the phenomenon under study occurs, and in the other it does not occur; Moreover, the second case differs from the first only in one circumstance, and all others are similar.

The method of difference is called the method of finding the different in the similar, because the compared cases coincide with each other in many properties.

The method of difference is used both in the process of observing phenomena in natural conditions, and in the conditions of a laboratory or production experiment. In the history of chemistry, many substances were discovered by the difference method - reaction accelerators, which later became known as catalysts. In agricultural production, this method checks, for example, the effectiveness of fertilizers.

In biology and medicine, the difference method is used in the study of the effects on the body of various substances and drugs. For these purposes, control and experimental groups of plants, experimental animals or people are distinguished. Both groups are kept in the same conditions - A, B, C. Then a new circumstance is introduced into the experimental group - M. The subsequent comparison shows that the experimental group differs from the control group with a new result - d. Hence it is concluded that M seems to be the cause of d.

The scheme of reasoning according to the method of difference has the following form:

1) ABCM calls d;

2) ABC doesn't call d.

Apparently, M is the cause of d.

Reasoning by the method of difference also presupposes a number of premises.

1. General knowledge is required about the antecedents, each of which may be the cause of the phenomenon under study. In the above diagram, these are circumstances A, B, C, M, which make up a disjunctive set:

A ∨ B ∨ C ∨ M.

2. Circumstances that do not satisfy the condition of sufficiency for the action under study should be excluded from the members of the disjunction. In the above scheme, A, B and C are subject to elimination, since their presence in the second case does not cause d. The result of the exclusion is expressed in a negative proposition: "Neither A, nor B, nor C is the cause of d." Elimination in reasoning by the method of difference also forms a negative knowledge of what could not have caused the phenomenon under study.

3. Among the many possible causes, there remains the only circumstance that is considered as a real cause. In the above diagram, the only circumstance is M, which is the cause of A.

Reasoning according to the method of difference acquires demonstrative knowledge only if there is an exact and complete knowledge of the previous circumstances that make up a closed disjunctive set.

Since, under the conditions of empirical knowledge, it is difficult to lay claim to an exhaustive statement of all circumstances, conclusions by the method of difference in most cases give only problematic conclusions. According to the recognition of many researchers, the most plausible inductive conclusions are achieved by the method of difference.

60. THE METHOD OF ACCOMPANYING CHANGE AS A METHOD OF SCIENTIFIC INDUCTION

The method is used in the analysis of cases in which there is a modification of one of the preceding circumstances, accompanied by a modification of the action under study..

Not all causally related phenomena allow the neutralization or replacement of individual factors that make them up. For example, when investigating the effect of friction on the velocity of a body, it is impossible in principle to exclude friction itself.

The only way to discover causal relationships under such conditions is to record concomitant changes in antecedent and subsequent phenomena in the process of observation. The cause in this case is such an antecedent circumstance, the intensity or degree of change of which coincides with the change in the action under study. If we denote by symbols A, B, C the preceding circumstances, each of which cannot be omitted or replaced; indices 1, 2, n - the degree of change in these circumstances; symbol d - the action of interest to us, then the reasoning by the method of accompanying changes takes the following form:

1) ABC1 calls d1;

2) ABC2 calls d2;

....................................

n) AVSp causes dn.

Apparently C is the cause of d. The application of the method of concomitant changes also implies the fulfillment of a number of conditions.

1. Knowledge of all possible causes of the phenomenon under study is necessary.

2. Of the given circumstances, those that do not satisfy the property of unambiguous causation should be eliminated.

3. Among the preceding ones, the only circumstance is singled out, the change of which accompanies the change of the action.

Concomitant changes can be direct and reverse.

Direct dependency means: the more intense the manifestation of the preceding factor, the more actively the phenomenon under study also manifests itself, and vice versa - with a decrease in intensity, the activity or degree of manifestation of the action decreases accordingly. For example, with an increase in air temperature, mercury expands, and its level in the thermometer rises, with a decrease in temperature, the mercury column falls accordingly.

Inverse relationship expressed in the fact that the intense manifestation of the preceding circumstance slows down the activity or reduces the degree of change in the phenomenon under study. For example, the greater the friction, the lower the speed of the body.

The validity of the conclusion in the conclusion according to the method of accompanying changes is determined by the number of cases considered, the accuracy of knowledge about the antecedent circumstances, as well as the adequacy of the changes in the antecedent circumstance and the phenomenon under study.

The validity of the conclusion also largely depends on the degree of correspondence between the changes in the preceding factor and the action itself. Not any, but only proportionally increasing or decreasing changes are taken into account. Those of them that do not differ in one-to-one regularity often arise under the influence of uncontrolled, random factors and can mislead the researcher.

61. THE METHOD OF REMAINS AS A METHOD OF SCIENTIFIC INDUCTION

The application of the method is associated with identifying the cause that causes a certain part of a complex action, provided that the causes that cause other parts of this action have already been identified.

The scheme of reasoning by the method of residuals has the following form:

1. ABC calls xyz.

2. A calls x.

3. B calls y. C calls z.

In the practice of scientific and ordinary reasoning, a modified conclusion by the method of residuals is often encountered, when, according to a known action, one concludes the existence of a new cause in relation to an already known one. For example, Maria Sklodowska-Curie, having established that some uranium ores emit radioactive rays exceeding the intensity of uranium radiation, came to the conclusion that these compounds contain some new substances. So new radioactive elements were discovered: polonium and radium.

Like other inductive inferences, the method of residuals generally yields problematic knowledge. The degree of probability of the conclusion in such a conclusion is determined, firstly, by the accuracy of knowledge about the previous circumstances, among which the cause of the phenomenon under study is being searched, and secondly, by the accuracy of knowledge about the degree of influence of each of the known causes on the overall result. An approximate and inaccurate list of antecedent circumstances, as well as an inaccurate idea of the influence of each of the known causes on the cumulative effect, can lead to the fact that in the conclusion of the conclusion, not a necessary, but only a concomitant circumstance will be presented as an unknown cause.

Residual reasoning is often used in the process of investigating crimes, mainly in cases where it is established that the causes are clearly disproportionate to the actions under investigation. If the action in its volume, scale or intensity does not correspond to a known reason, then the question is raised about the existence of some other circumstances.

For example, in a criminal case on the theft of goods from a warehouse, the accused admitted the fact of theft and testified that he alone took the stolen item out of the warehouse. The inspection carried out found that it was beyond the power of one person to carry such a heavy thing. The investigator came to the conclusion about the participation in the theft of other persons, in connection with which the qualification of the act also changed.

The considered methods of establishing causal relationships in their logical structure belong to complex reasoning, in which proper inductive generalizations are built with the participation of deductive conclusions. Based on the properties of a causal connection, deduction acts as a logical means of eliminating (excluding) random circumstances, thereby logically correcting and directing inductive generalization.

The relationship of induction and deduction ensures the logical consistency of reasoning when applying methods, and the accuracy of the knowledge expressed in the premises determines the degree of validity of the conclusions obtained.

62. CONCLUSION BY ANALOGY: ESSENCE AND LOGICAL STRUCTURE

In science and practical affairs, the object of research is often single events, objects and phenomena that are unique in their individual characteristics. When explaining and evaluating them, it is difficult to use both deductive and inductive reasoning. In this case, they resort to the third method of reasoning - inference by analogy: liken a new single phenomenon to another, known and similar single phenomenon and extend previously received information to the first.

For example, a historian or politician, analyzing revolutionary events in a particular country, likens them to a similar revolution previously committed in another country and, on this basis, predicts the development of political events. Thus, Russian politicians substantiated their idea of the need to conclude a peace treaty with Germany in 1918 (Brest Peace) by referring to a similar historical situation at the beginning of the 1807th century, when the Germans themselves concluded an enslaving treaty with Napoleon in 6 (Tilsit peace), and then after 7-XNUMX years, having gathered their strength, they came to their liberation. A similar solution was proposed for Russia.

The conclusion in the history of physics proceeded in the same form, when, in elucidating the mechanism of sound propagation, it was likened to the motion of a liquid. On the basis of this assimilation, the wave theory of sound arose. In this case, the objects of assimilation were liquid and sound, and the transferred attribute was the wave method of their propagation.

Inference by analogy is a conclusion about the belonging of a certain feature to the individual object under study (object, event, relation or class) based on its similarity in essential features with another already known individual object.

Inference by analogy is always preceded by the operation of comparing two objects, which allows you to establish similarities and differences between them. At the same time, for analogy, not any coincidences are required, but similarities in essential features with insignificant differences. It is these similarities that serve as the basis for likening two material or ideal objects.

The logical transition from known to new knowledge is regulated in the conclusions by analogy by the following rule: if two individual objects are similar in certain characteristics, then they may be similar in other characteristics found in one of the objects being compared.

63. TYPES OF ANALOGY. ANALOGY OF OBJECTS AND ANALOGY OF RELATIONS

By the nature of the objects being compared There are two types of analogy:

1) analogy of objects and 2) analogy of relationships.

1. Analogy of objects - a conclusion in which the object of assimilation is two similar single objects, and the transferred sign - properties of these items.

If we denote two single objects or events with the symbols a and b, and P, Q, S, T are their signs, then the conclusion by analogy can be represented by the following scheme:

and are inherent in P, Q, S, T;

b inherent P, Q, S;

b is inherent in T.

An example of such an analogy is the explanation in the history of physics of the mechanism of light propagation. When physics faced the question of the nature of light motion, the Dutch physicist and mathematician of the XNUMXth century. Huygens, based on the similarity of light and sound in such properties as their rectilinear propagation, reflection, refraction and interference, likened light motion to sound and came to the conclusion that light also has a wave nature.

The logical basis for the transfer of attributes in analogies of this kind is the similarity of likened objects in a number of their properties.

2. Relationship analogy - a conclusion in which the object of assimilation is a similar relationship between two pairs of objects, and the transferred attribute - properties of these relations.

For example, two pairs of persons x and y, m and n are in the following relationships:

1) x is the father (relation R1) of y’s minor son;

2) m is the grandfather (R2 ratio) and the only relative of the minor grandson n;

3) it is known that in the case of parental relations (R1) the father is obliged to support his minor child. Taking into account a certain similarity between the relations R1 and R2, we can conclude that R2 is also characterized by the noted property, namely, the obligation of the grandfather to support the grandson in a certain situation. The conclusion by analogy of relations can be represented by the following scheme:

1) xR1y R1 are inherent in P, Q, S, T;

2) mR2y R2 inherent P, Q, S.

Apparently, R2 is inherent in T.

When turning to the analogy of relations, one should keep in mind the peculiarities of this conclusion and not confuse it with conclusions based on the analogy of objects. If in the latter two individual events or phenomena are likened, then in the first the objects themselves are not compared and may not even allow for likening. Assimilating the relation between x and y to the relation between m and n does not mean that x must be similar to m and y must be similar to n. It is important that the relationship between the first pair of objects (mR1n) be similar to the relationship between the objects of the second pair (mR2n). An incorrect understanding of conclusions based on the analogy of relations sometimes leads to a logical error, the essence of which is the unfounded identification not of relations (R1 and R2), but of the objects themselves: x is identified with m, and y with n.

64. TYPES OF ANALOGY. SUBSTANTIATION OF CONCLUSIONS BY ANALOGY OF RELATIONSHIPS. Strict and non-strict analogy

Validity of conclusions by analogy of relations depends on the following conditions:

1. The conclusion will be valid only if a real similarity is revealed and recorded, which should not be approximate, not accidental, but strictly defined and specific similarity in essential features. The absence of such a similarity renders the inference by analogy untenable.

2. Taking into account the differences between like objects is the second important condition for the consistency of conclusions by analogy. In nature, there are no absolutely similar phenomena: the highest degree of similarity always implies differences. This means that in any case of assimilation, there are also differences between the compared objects. Differences can be insignificant, i.e., compatible with the transferred attribute, and significant, i.e., preventing the transfer of the attribute from one object to another.

3. The degree of validity of conclusions by analogy depends on the quality of the connection between similar and transferred features. Distinguish between strict and non-strict analogy.

Strict analogy. Its distinctive feature - necessary connection of the transferred characteristic with similarity characteristics.

A non-strict analogy is such an assimilation in which the relationship between similar and transferred features is thought of as necessary only with a greater or lesser degree of probability. In this case, having found signs of similarity in another object, it is possible only in a logically weakened, i.e. problematic, form to conclude that the transferred attribute belongs to it.

A loose analogy is often found in socio-historical research, because here it is extremely difficult to establish a connection between phenomena that would strictly indicate all the ensuing consequences.

Conditions that increase the likelihood of conclusions in a non-strict analogy are:

1) the similarity of the objects being compared in a significant number of essential features - the more significant similarities, the more thorough the conclusion by analogy;

2) the absence of significant differences between the objects being compared;

3) the degree of probability of knowledge of the relationship between similar and transferable characteristics.

In cases where an insufficient number of similar features are found in the compared objects, or when the relationship between similar and transferred features is established in a weak form, the conclusion by analogy, due to insufficient validity, can only give an unlikely conclusion. If this does not take into account the signs of difference, then such an analogy cannot be regarded otherwise than as superficial. The true conclusion in such a conclusion can only be accidental.

65. THE ROLE OF ANALOGY IN SCIENCE

Analogy can rightly be called a form of inference that was widely used in the early stages of the development of thinking. Analogy is a frequent form of inference in the reasoning of a child, whose thinking in its development repeats in a concise form the history of the development of human thinking as a whole.

The history of the development of science and technology shows that analogy has served as the basis for many scientific and technical discoveries. Faraday's brilliant guess about the physical existence of magnetic lines similar to electric lines, as well as the analogy he drew between the magnet and the Sun, on the one hand, and light rays and magnetic lines, on the other, served as a program for further research and discoveries by Maxwell, Herschel, Lebedev, Popov and other scientists.

An important role in modern science is played by the modeling method, which is based on inference by analogy. It is used in shipbuilding, aerodynamics, hydraulic engineering, cybernetics, etc.

Inference by analogy plays a special role in the socio-historical sciences, often acquiring the significance of the only possible method of research. Not having sufficient factual material, the historian often explains little-known facts, events and situations by likening them to previously studied events and facts from the life of other peoples in the presence of similarities in the level of development of the economy, culture, and political organization of society.

The role of inference by analogy in political science and politics is essential in the development of strategic tasks and the determination of a tactical line in the specific conditions of socio-political development.

Analogy is used in special cases of legal assessment, as well as in the process of investigating crimes and conducting forensic examinations.

66. THE ROLE OF ANALOGY IN THE LEGAL PROCESS

Analogy in legal assessment. In some legal systems, legal assessment is allowed by analogy of the law or by precedent.

Based on the practical difficulty of foreseeing and listing in the law all specific types of legal relations that may arise in the future, the legislator grants the court the right to evaluate cases not provided for by law according to the rules that govern similar legal relations. This is the essence of the legal institution of analogy of law.

In the Russian legal system, the analogy of the criminal law is not provided. It operates only in civil law, which is explained by the practical difficulty of foreseeing in the system of law all new types of civil law relations that may arise in the future.

According to theory and legal practice, the assessment of civil legal relations by analogy with the law is allowed only if certain conditions are met:

1) there is a requirement that there is no norm in the legal system that would directly provide for this type of relationship;

2) a rule of law applied by analogy must provide for relations that are similar in their essential features and the differences are insignificant.

Legal assessment proceeds in the form of inference by analogy and in the case of a precedent in legal proceedings, when the court, in its conclusions about the grounds and limits of legal liability in a particular case, relies on a decision previously made by the court in a similar case.

Such assimilation cannot claim to be demonstrative. Every offense, especially

in the field of criminal law, it is a strictly defined set of objective and subjective circumstances that requires a specific assessment and a strictly individual approach to choosing a punishment. The reference to judicial precedent often levels out the differences and thus does not ensure legal justice. That is why the appeal to judicial precedent, which is practiced, for example, in the Anglo-American legal system, has never been recognized in theory and practice as a sufficiently reliable source of law. In Russian history, judicial law has never attached importance to precedent as a source of law.

Analogy in the investigation process. When analyzing factual material, the judge and investigator turn to individual experience - their own and others. Comparing a specific case with previously studied individual cases helps to clarify the similarities between them and, on this basis, by likening one event to another, to discover previously unknown signs and circumstances of the crime.

In its most distinct form, inference by analogy is found in the disclosure of crimes by the way they were committed.

The probable nature of the knowledge obtained with the help of analogy predetermines the unequal role of this conclusion at various stages of forensic research. So, in the process of preliminary investigation and judicial investigation, the appeal to analogy is quite legitimate, here it performs a heuristic function - it serves as an incentive for reflection, acts as a logical basis for building versions.

67. HYPOTHESIS, ITS STRUCTURE AND CONDITIONS OF SCIENTIFIC CONSISTENCY

Hypothesis - this is a natural form of knowledge development, which is an informed assumption put forward in order to clarify the properties and causes of the phenomena under study. A hypothesis is a decisive link in the cognitive chain that ensures the formation of new knowledge.

The hypothesis includes the following elements:

1) initial data, or grounds;

2) assumption;

3) logical processing of initial data and transition to an assumption;

4) testing a hypothesis, turning an assumption into reliable knowledge or refuting it.

Principles for constructing a hypothesis

The principle of objectivity of research, which can be interpreted in two ways: psychological (the absence of bias, when the researcher is guided by the interests of establishing the truth, and not by his own subjective inclinations, preferences and desires) and logical and methodological (comprehensiveness of research in order to establish the truth).

First, when putting forward a hypothesis or version, all the initial empirical material should be taken into account.

Secondly, comprehensiveness requires the construction of all possible versions under specific conditions. This requirement is dictated by the use of the method of "multiple hypotheses" known in science. Since the primary material in any empirical study, as a rule, is incomplete, it thereby gives an idea only of individual links, individual dependencies between phenomena. In order to reveal the entire chain of relationships, it is necessary to build a number of versions that explain the unknown circumstances of the crime in different ways.

To build the most plausible version, ignoring the others, is to approach the matter one-sidedly. This threatens that the investigator is captured by the facts, and if in some cases the passion for one version only delays the investigation in time, then in others it can lead to a miscarriage of justice.

Conditions for the validity of the hypothesis

A hypothesis in science, like a version in a forensic study, is considered valid if it satisfies the following logical and methodological requirements.

The hypothesis must be consistent. This means that assumption H should not contradict the original empirical basis, and also should not contain internal contradictions.

The hypothesis must be fundamentally testable, and if we talk about the judicial version, it must be subject to verification by facts. The fundamental untestability of the hypothesis dooms it to eternal problematicness and makes it impossible to turn into reliable knowledge.

A hypothesis is considered valid if it is empirically and theoretically substantiated. The probability of a hypothesis depends on the degree of its validity and is determined using quantitative or qualitative evaluation standards.

The cognitive, or heuristic, value of a hypothesis is determined by its informativeness, which is expressed in the predictive and explanatory power of the hypothesis.

68. CLASSIFICATION OF HYPOTHESES BY COGNITIVE FUNCTIONS

Hypotheses differ in their cognitive functions and in the object of study.

Functions in the cognitive process There are hypotheses: descriptive and explanatory.

Descriptive hypothesis - this is an assumption about the inherent properties of the object under study. It usually answers the question: “What is this object?” or “What properties does this item have?”

Descriptive hypotheses can be put forward in order to identify the composition or structure of an object, reveal the mechanism or procedural features of its activity, and determine the functional characteristics of an object.

Thus, for example, the hypothesis about the wave propagation of light that arose in the theory of physics was a hypothesis about the mechanism of light motion. The chemist's assumption about the components and atomic chains of the new polymer refers to hypotheses about the composition and structure. The hypothesis of a political scientist or lawyer, predicting the immediate or distant social effect of the adopted new package of laws, refers to functional assumptions.

A special place among descriptive hypotheses is occupied by hypotheses about the existence of an object, which are called existential hypotheses. An example of such a hypothesis is the assumption that the continent of the western (America) and eastern (Europe and Africa) hemispheres once co-existed. The same will be the hypothesis of the existence of Atlantis.

An explanatory hypothesis is an assumption about the reasons for the emergence of the object of research. Such hypotheses usually ask: "Why did this event happen?" or “What are the reasons for the appearance of this item?”.

Examples of such assumptions: the hypothesis of the Tunguska meteorite; the hypothesis of the appearance of ice ages on Earth; assumptions about the causes of extinction of animals in various geological epochs; hypotheses about the motives and motives for committing a specific crime by the accused, etc.

The history of science shows that in the process of knowledge development, existential hypotheses first arise, clarifying the fact of the existence of specific objects. Then there are descriptive hypotheses that clarify the properties of these objects. The last step is the construction of explanatory hypotheses that reveal the mechanism and causes of the emergence of the objects under study.

69. CLASSIFICATION OF HYPOTHESES BY THE OBJECT OF STUDY

Hypotheses differ in their cognitive functions and in the object of study.

By object of study There are hypotheses: general and particular.

A general hypothesis is an educated guess about natural relationships and empirical regularities.. Examples of general hypotheses include: developed in the 18th century. M.V. Lomonosov's hypothesis about the atomic structure of matter; modern competing hypotheses of academician O.Yu. Schmidt and academician V.G. Fesenkova on the origin of celestial bodies; hypotheses about the organic and inorganic origin of oil, etc.

General hypotheses play the role of scaffolding in the development of scientific knowledge. Once proven, they become scientific theories and are a valuable contribution to the development of scientific knowledge.

Private hypothesis - this is an educated guess about the origin and properties of individual facts, specific events and phenomena. If a single circumstance served as the cause of the emergence of other facts and if it is not accessible to direct perception, then its knowledge takes the form of a hypothesis about the existence or properties of this circumstance.

Particular hypotheses are put forward both in the natural sciences and in the socio-historical sciences. Private hypotheses are also the assumptions that are put forward in forensic and investigative practice, because here one has to infer about single events, the actions of individuals, individual facts that are causally related to a criminal act.

Along with the terms "general" and "private" hypothesis in science, the term "working hypothesis" is used.

A working hypothesis is an assumption put forward at the first stages of the study, which serves as a conditional assumption that allows us to group the results of observations and give them an initial explanation.

The specificity of the working hypothesis lies in its conditional and, therefore, temporary acceptance. It is extremely important for the researcher to systematize the available factual data at the very beginning of the investigation, rationally process them and outline the paths for further searches. The working hypothesis just performs the function of the first systematizer of facts in the process of research.

From a working hypothesis, it can turn into a stable and fruitful one. At the same time, it can be replaced by other hypotheses if its incompatibility with new facts is established.

70. VERSION AS A VARIETY OF HYPOTHESIS

In historical, sociological or political research, as well as in judicial and investigative practice, when explaining individual facts or a set of circumstances, a number of hypotheses are often put forward that explain these facts in different ways. Such hypotheses are called versions (from Latin - modify).

version in court proceedings - one of the possible hypotheses explaining the origin or properties of individual legally significant circumstances or the crime as a whole.

When investigating crimes and litigation, versions are built that are different in content and coverage of the circumstances. Among them, there are general and private versions.

General version - this is an assumption that explains all crimes as a whole as a single system of specific circumstances. She answers not one, but many interrelated questions, clarifying the entire set of legally significant circumstances of the case. The most important among these questions will be: what crime was committed? who did it? where, when, under what circumstances and in what way was it committed? What are the goals, motives of the crime, and the guilt of the criminal?

The unknown real reason about which the version is created is not the principle of development or an objective pattern, but a specific set of actual circumstances that make up a single crime. Covering all the issues to be clarified in court, such a version bears the features of a general summarizing assumption that explains the entire crime as a whole.

A private version is an assumption that explains individual circumstances of the crime in question.. Being unknown or little-known, each of the circumstances can be the subject of independent research; for each of them, versions are also created that explain the features and origin of these circumstances.

Examples of private versions can be the following assumptions: about the whereabouts of stolen items or about the whereabouts of the offender; about the accomplices of the act; about the method of penetration of the offender to the place of the act; about the motives for committing a crime, and many others.

Private and general versions are closely interconnected with each other in the process of investigation. The knowledge obtained with the help of private versions serves as the basis for constructing, concretizing and clarifying the general version explaining the criminal act as a whole. In turn, the general version makes it possible to outline the main directions for putting forward private versions about the circumstances of the case that have not yet been identified.

71. STAGES OF DEVELOPING A HYPOTHESIS (VERSION)

Building a version in a forensic study consists of three stages:

1. Analysis of individual facts and relationships between them

The purpose of the analysis is to single out among the many factual circumstances those that are directly or indirectly, explicitly or implicitly, closely or remotely related to the criminal event.

The inferences by which facts are analyzed depend both on the characteristics of the facts themselves and on the nature of previously acquired knowledge. If the investigator resorts to general knowledge, his conclusion proceeds in the form of deductive reasoning. The initial assumptions of such syllogisms are either scientifically proven provisions or empirical generalizations obtained in judicial and investigative practice.

The analysis of facts can also proceed in the form of induction. For example, based on similar features of handwriting in a number of anonymous slanderous written statements, the investigator made a presumable generalizing conclusion that they were all written by the same person.

Generalization at this level solves an important problem: from the set of investigated facts, only those are selected that give grounds for assuming their connection with the crime.

2. Synthesis of facts and their generalization

Synthesis is the mental unification of analytically isolated facts into a unity, abstracted from random circumstances.

The discovery of the relationship between facts, the direction and sequence of this relationship make it possible to restore the entire chain of causal connection, to know those facts that lie at the beginning of this chain and which led to the emergence of all other circumstances. The synthesis of facts into a single system is the main prerequisite for constructing a hypothesis, or version.

3. Assumption

The problematic conclusion is due to the fact that the hypothesis is only partially derivable from the premises. Insufficient justification means that if the premises are true, the conclusion can be either true or false. The degree of probability of a hypothesis is determined in this case by the degree of its meaningful substantiation by facts.

In a forensic study, where versions of single events are built, their probability cannot be expressed as a number, but usually takes on the values: “very likely”, “more likely”, “equally likely”, “unlikely”, etc.

Hypothesis testing. The hypothesis is tested in two stages:

1. Deductive derivation of the consequences arising from the hypothesis. Allows you to rationally build the entire investigation process. The version in the forensic research serves as a logical basis for planning operational and investigative work.

2. Comparison of consequences with facts in order to refute or confirm the hypothesis.

The refutation of the version proceeds by discovering facts that contradict the consequences derived from it. A hypothesis or version is confirmed if the consequences derived from it coincide with the newly discovered facts.

72. WAYS OF PROOFING HYPOTHESES

The main methods of proving hypotheses are: deductive justification of the assumption expressed in the hypothesis; direct detection of objects assumed in the hypothesis; logical proof of the hypothesis.

Direct detection of the desired items. Particular hypotheses in science and versions in forensic research often aim to identify the fact of the existence of specific objects and phenomena at a certain time and in a certain place, or answer the question about the properties and qualities of such objects. The most convincing way to transform such an assumption into reliable knowledge is the direct discovery at the assumed time or in the assumed place of the sought-after objects or the direct perception of the assumed properties.

For example, when investigating criminal cases of theft, an important task is the discovery of stolen valuables. These values are usually hidden or realized by criminals. In this regard, there are private versions about the whereabouts of such things and values.

Versions proven by direct discovery of the alleged cause are always private. With their help, as a rule, only individual factual circumstances of the case, particular aspects of the crime event are established.

Logical proof of versions. Versions that explain the essential circumstances of the cases under investigation are transformed into reliable knowledge through logical justification. It proceeds in an indirect way, because events that took place in the past or phenomena that exist at the present time, but are inaccessible to direct perception, are cognized. This is how they prove, for example, versions about the method of committing a crime, about guilt, about the motives for committing a crime, the objective circumstances under which the act was committed, etc.

The logical proof of a hypothesis, depending on the method of justification, can proceed in the form of indirect or direct proof.

Indirect proof proceeds by refuting and excluding all false versions, on the basis of which they assert the reliability of the only remaining assumption.

The conclusion in this conclusion can be regarded as reliable if, firstly, an exhaustive series of versions is built to explain the event under study, and, secondly, all false assumptions are refuted in the process of checking versions. The version pointing to the remaining reason will be the only one in this case, and the knowledge expressed in it will no longer act as problematic, but as reliable.

Direct proof of a hypothesis proceeds by deriving various consequences from the assumption, but arising only from this hypothesis, and confirming them with newly discovered facts.

In the absence of indirect proof, a simple coincidence of facts with those consequences that are derived from the version cannot be regarded as a sufficient basis for the truth of the version, because the coinciding facts could also be caused by another reason.

73. THE ESSENCE OF LOGICAL PROOF AND ITS STRUCTURE

Доказательство - a logical operation of justifying the truth of a judgment with the help of other true and related judgments.

The term "evidence" in procedural law is used in two senses:

▪ to designate factual circumstances that act as carriers of information about significant aspects of a criminal or civil case (for example, traces left at the scene of a crime);

▪ to indicate sources of information about factual circumstances relevant to the case (eg, testimony of witnesses).

The requirement of proof is also imposed on knowledge in legal proceedings: a judgment in a criminal or civil case is considered just if it received an objective and comprehensive justification during the trial. Proof is one of the varieties of the process of argumentation.

Argumentation is the operation of substantiating any judgments, in which, along with logical ones, speech, emotional-psychological and other extra-logical methods and techniques of persuasive influence are also used..

Structure of the proof. The proof includes three interrelated elements:

1. Thesis It is a proposition that needs to be proven true. The thesis is the main structural element of the argument and answers the question: what is justified?

2. Arguments or reasons, are the initial theoretical or factual provisions with the help of which the thesis is substantiated. They serve as the basis, or logical foundation of the argument, and answer the question: with what, with what help is the thesis substantiated?

Judgments can be used as arguments:

1) theoretical generalizations. For example, the physical laws of gravity make it possible to calculate the flight path of a specific cosmic body and serve as arguments confirming the correctness of such calculations.

The role of arguments can also be played by empirical generalizations;

2) judgments about facts.

Facts, or actual data, are called single events or phenomena, which are characterized by a certain time, place and specific conditions of occurrence and existence;

3) axioms, i.e. obvious and therefore not proven in the given field of position;

4) definitions of the basic concepts of a particular field of knowledge.

3. Demonstration or form of proof - it is a logical connection between arguments and thesis.

The logical transition from arguments to a thesis proceeds in the form of a conclusion. This may be a separate conclusion, but more often their chain. The premises in the conclusion are judgments in which information about the arguments is expressed, and the conclusion is a judgment about the thesis. To demonstrate means to show that the thesis logically follows from the accepted arguments according to the rules of the corresponding inferences.

74. DIRECT JUSTIFICATION OF THE THESIS

According to the method of proof, two types of substantiation of the put forward position are distinguished: direct and indirect.

Direct is the substantiation of a thesis without resorting to assumptions competing with the thesis..

Direct justification may take the form of deductive reasoning, induction, or analogy, which are used alone or in various combinations.

Deductive justification most often expressed in summing up a particular case under a general rule. The thesis about the belonging or non-belonging of a certain attribute to a specific object or phenomenon is justified by reference to the known laws of science, empirical generalizations, moral or legal prescriptions, to obvious axiomatic provisions or previously accepted definitions. They express these propositions in a larger premise and, relying on them as grounds, judge specific facts, knowledge of which is fixed in a minor premise.

The peculiarity of deductive justification is that if the premises-arguments are true, as well as if the rules of inference are observed, it gives reliable results. The truth of the thesis in this case necessarily follows from the premises. In addition, thanks to the generalizing argument presented in the larger premise, deductive reasoning also performs an explanatory or evaluative function. This enhances the persuasive power of deductive reasoning.

Inductive justification - this is a logical transition from arguments that provide information about individual cases of a certain kind, to a thesis that generalizes these cases.

Inductive justification is often resorted to when analyzing the results of observations and experimental data, when operating with statistical materials. The specificity of inductive justification lies in the fact that, as a rule, actual data act as arguments here. With the right approach to the facts, inductively constructed argumentation has a very high persuasive power.

Justification in the form of an analogy - this is a direct justification of the thesis, in which a statement is formulated about the properties of a single phenomenon. Analogy as a method of justification is used in the natural and social sciences, in technology, and in the practice of ordinary reasoning. Here she gives, as a rule, problematic conclusions. The modeling method in various fields of technology provides logically sound results if theoretically justified similarity criteria are developed. Analogy as a plausible, but the only possible method of justification is resorted to in historical research. Based on the assimilation, the conclusions of experts in fingerprinting, tracing and other types of forensic examinations are built.

75. INDIRECT JUSTIFICATION OF THE THESIS

Indirect is the substantiation of a thesis by establishing the falsity of the antithesis or other assumptions competing with the thesis..

The difference in the structure of competing assumptions determines two types of indirect justification: apagogic and disjunctive.

Apagogical they call the justification of the thesis by establishing the falsity of the assumption that contradicts it - the antithesis. The proof in this case is constructed in three stages:

1. If there is a thesis, they put forward a position that contradicts it - antithesis; conditionally recognize it as true (admission of indirect evidence) and deduce the consequences that logically follow from it.

The thesis and antithesis can be expressed in the form of different judgments. So, for the thesis in the form of a single affirmative judgment "N. is guilty of committing this crime," the antithesis will be the denial of this judgment: "N. is not guilty of committing this crime." An antithesis for a single affirmative judgment can also be an affirmative judgment if it deals with incompatible properties of the same phenomenon. For example, the relation of contradiction takes place between the thesis "The crime is committed intentionally" and the antithesis "The crime is committed carelessly."

If the thesis is represented by a universally affirmative proposition - "All S are P", then the antithesis will be a particular negative proposition that contradicts it: "Some S are not P". For the general negative thesis "No S is P", the antithesis is the particular affirmative: "Some S are P". Thus, the thesis is drawn up in accordance with the rules of the relationship between judgments.

2. The consequences logically derived from the antithesis are compared with the provisions, the truth of which was previously established. In case of non-coincidence, these consequences are abandoned.

3. From the falsity of the consequences, one logically concludes that the assumption is false.

As a result, from the falsity of the assumption, they conclude on the basis of the law of double negation about the truth of the thesis.

The apagogic type of indirect justification is used only if the thesis and antithesis are in relation to contradiction. With other types of incompatibility, including opposition, the apagogical justification becomes untenable.

Dividing called the indirect justification of the thesis, which is a member of the disjunction, by establishing the falsity and excluding all other competing members of the disjunction.

The substantiation of the thesis is built in this case by the method of elimination. In the process of argumentation, they show the failure of all members of the disjunction, except for one, thereby indirectly substantiating the truth of the remaining thesis.

A disjunctive justification is valid only if the disjunctive judgment is complete or closed. If not all solutions are considered, then the elimination method does not ensure the reliability of the thesis, but only gives a problematic conclusion.

Divisive argumentation, including evidence, is often used in forensic and investigative practice when checking versions regarding the perpetrators of a particular crime, when explaining the causes of specific phenomena, and in many other cases.

76. CRITICISM, ITS FORMS AND METHODS

Criticism - this is a logical operation aimed at destroying a previously held argumentation process. The form of expression can be implicit or explicit.

Implicit criticism - this is a skeptical assessment of the thesis without a specific analysis of the shortcomings and an accurate indication of weaknesses. Doubt in this case is expressed approximately in the following form: "Your ideas seem doubtful to me," etc.

Explicit criticism - an indication of specific shortcomings of the thesis. There can be three types of orientation: destructive, constructive and mixed.

Destructive is criticism aimed at destroying a thesis, argument or demonstration.

1. Criticism of the thesis. The thesis is regarded as deliberately false. Let us consider a direct refutation of the thesis, which is constructed in the form of an argument called “reduction to absurdity.” First, the truth of the put forward conditionally is assumed and the consequences logically following from it are derived. If, when comparing the consequences with the facts, it turns out that they contradict objective data, then they are thereby declared invalid. On this basis, they note the inconsistency of the thesis itself, reasoning according to the principle: false consequences always indicate the falsity of their basis.

2. Criticism of the arguments. It can be expressed in the fact that the opponent points out an inaccurate statement of facts, the ambiguity of the procedure for summarizing statistical data, expresses doubts about the authority of the expert whose conclusion is referred to, etc. Doubts about the correctness of the arguments are transferred to the thesis, which logically follows from the arguments and is also regarded as dubious. If the arguments are established to be false, the thesis is unconditionally considered unfounded and requires new, independent confirmation. 3.

Criticism of the demonstration. Show that there is no logical connection between the arguments and the thesis. If the thesis does not follow from the arguments, then it is considered unfounded. The initial and final points of reasoning are out of logical connection with each other.

Successful criticism of a demonstration presupposes a clear understanding of the rules and errors of the corresponding conclusions: deduction, induction, analogy, in the form of which the justification of the thesis proceeds.

Both the criticism of the arguments and the criticism of the demonstration in themselves only destroy the argument and show the groundlessness of the thesis. In this case, the thesis can be said that it is not based on arguments or is based on poor-quality arguments and requires a new justification.

Constructive criticism is the substantiation of one's own thesis in order to refute an alternative statement.

Constructive criticism requires the following:

Clearly and comprehensively present the thesis of your speech.

Show that this thesis is not only different from the proposed one, but contradicts it as an alternative one.

Concentrate efforts on the selection of arguments in favor of the proposed thesis for maximum evidentiary impact.

Mixed refers to criticism that combines constructive and destructive approaches.

77. BASIC RULES OF LOGICAL EVIDENCE AND ERRORS POSSIBLE IN THEIR VIOLATION. RULES AND ERRORS RELATED TO THE THESIS

Logical reasoning presupposes the observance of two rules in relation to the thesis: the certainty of the thesis and the immutability of the thesis.

Certainty of the thesis

The rule of certainty means that the thesis must be formulated clearly and clearly. The requirement for certainty, a clear identification of the meaning of the propositions put forward, applies equally to both the presentation of one’s own thesis and the presentation of the criticized position - the antithesis. In ancient Indian philosophy, there was a reasonable rule: if you are going to criticize someone’s position, then you should repeat the thesis being criticized and obtain the consent of the opponent present that his thought was presented correctly. Only after this can a critical analysis begin. The thought of an absent opponent can be accurately expressed with the help of a quotation. Following this rule makes criticism objective, accurate and unbiased.

A clear definition of the thesis involves the following steps: identifying the meaning of the terms used; analysis of the judgment, in the form of which the thesis is presented: identification of the subject and predicate of the judgment, the quality of the judgment (contains an assertion in it or something is denied); clarification of the quantitative characteristics of the judgment.

The thesis can be represented by a quantitatively indefinite statement. For example, "People are selfish" or "People are arrogant." In this case, it is not clear whether all or some people are referred to in the statement. This kind of theses is difficult to defend and no less difficult to refute precisely because of their logical uncertainty.

Of great importance is the question of the modality of the thesis: is this judgment reliable or problematic; possible or actual; the thesis claims to be logical or factual truth, etc.

If the thesis is presented as a complex proposition, additional analysis of logical connectives is required.

The immutability of the thesis

The rule of immutability of the thesis prohibits modifying or deviating from the originally formulated position in the process of this reasoning. Failure to follow these rules leads to errors.

Thesis loss. This error manifests itself in the fact that, having formulated the thesis, they forget it and move on to another, directly or indirectly related to the first, but in principle a different position.

Thesis change. Substitution of the thesis can be complete or partial.

A complete substitution of the thesis often occurs as a result of delusion or slovenliness in reasoning, when the speaker does not first clearly and definitely formulate his main idea, but corrects and clarifies it throughout the speech.

Partial substitution of the thesis is expressed in the fact that during the speech they try to modify their own thesis, narrowing or softening the initially too general, exaggerated or overly harsh statement.

78. BASIC RULES OF LOGICAL EVIDENCE AND ERRORS POSSIBLE IN THEIR VIOLATION. RULES AND ERRORS RELATED TO ARGUMENTS

The following rules must be followed for arguments:

▪ reliability;

▪ justification independent from the thesis;

▪ consistency;

▪ sufficiency.

1. Violation of this logical rule leads to two errors: taking a false argument as true - called the "basic fallacy" and anticipating the foundation. The reasons for the first error are the use of a non-existent fact as an argument, a reference to an event that did not actually take place, an indication of non-existent eyewitnesses, etc. arbitrarily taken provisions: they refer to rumors, to current opinions or assumptions made by someone and pass them off as arguments that allegedly substantiate the main thesis.

2. Autonomous substantiation of arguments means: since the arguments must be true, then before substantiating the thesis, the arguments themselves should be checked. At the same time, grounds are sought for arguments, without referring to the thesis. Otherwise, it may turn out that unproven arguments are substantiated by an unproven thesis. This error is called "circle in demo".

3. The requirement of consistency of arguments follows from the logical idea, according to which anything formally follows from a contradiction - both thesis and antithesis. Substantially, not a single proposition necessarily follows from contradictory grounds.

4. The requirement of sufficiency of arguments is connected with a logical measure - in their totality, the arguments must be such that, according to the rules of logic, a thesis to be proved must necessarily follow from them.

The sufficiency of arguments should be regarded not in terms of their number, but in terms of their weight. At the same time, separate, isolated arguments, as a rule, have little weight, because they allow different interpretations. It is a different matter if a number of arguments are used that are interconnected and reinforce each other.

79. BASIC RULES OF LOGICAL EVIDENCE

The logical connection of arguments with the thesis proceeds in the form of such conclusions as deduction, induction and analogy. The logical correctness of the demonstration depends on the observance of the rules of the corresponding inferences.

1. The deductive method of argumentation involves the observance of a number of methodological and logical requirements. The most important include the following:

1) an exact definition or description in a larger premise that plays the role of an argument, the original theoretical or empirical position. In judicial research, individual legal provisions and articles of codes often act as generalizing arguments, on the basis of which a legal assessment of specific phenomena is given;

2) an accurate and reliable description of a specific event, which is given in the minor premise;

3) compliance with all the rules of categorical, conditional, dividing and mixed forms of syllogisms.

2. The inductive method of argumentation is used, as a rule, in cases where factual data are used as arguments. The evidentiary value of inductive justification depends on the stable recurrence of properties in homogeneous phenomena. The greater the number of favorable cases observed and the more diverse the conditions for their selection, the more solid the inductive argument. Most often, inductive justification leads only to problematic conclusions, because what is characteristic of individual objects is not always inherent in the entire group of phenomena. 3. Argumentation in the form of analogy is used in the case of assimilation of single events and phenomena.

Since the analogy of socio-historical phenomena does not always give unconditional and final conclusions, it can be used only as an addition to deductive or inductive justification.

80. DEMO ERRORS

Errors in the demo associated with the lack of a logical connection between the arguments and the thesis.

The absence of a logical connection between the arguments and the thesis is called the fallacy of "imaginary following".

The imaginary following often arises because of the discrepancy between the logical status of the premises in which the arguments are presented, and the logical status of the proposition containing the thesis. Let us point out typical cases of violation of the demonstration, regardless of the types of inferences used.

1. Logical transition from a narrow area to a wider area. The arguments, for example, describe the properties of a certain type of phenomena, while the thesis unreasonably refers to the properties of the entire type of phenomena, although it is known that not all features of a species are generic.

2. The transition from what has been said with a condition to what has been said unconditionally.

3. The transition from what was said in a certain relation to what was said without regard to anything else. So, following will be imaginary if, relying on problematic, even very probable arguments, they try to substantiate a reliable thesis.

The error of imaginary following also takes place in those cases when, to substantiate the thesis, arguments are given that are logically unrelated to the thesis under discussion. Among the many such tricks, we name the following:

Argument for strength. Instead of a logical substantiation of the thesis, they resort to extra-logical coercion - physical, economic, administrative, moral-political and other types of influence.

Argument for ignorance. Using the ignorance or ignorance of the opponent or listeners and imposing on them opinions that do not find objective confirmation or contradict science.

Argument for profit. Instead of a logical justification for the thesis, they agitate for its adoption because it is so beneficial in a moral-political or economic sense.

Reason for common sense. It is often used as an appeal to ordinary consciousness instead of a real justification. Although it is known that the concept of common sense is very relative, it is often deceptive, if it is not about household items.

An argument for compassion. It manifests itself in those cases when, instead of a real assessment of a particular act, they appeal to pity, philanthropy, compassion. This argument is usually resorted to in cases where it is a question of the possible conviction or punishment of a person for committed misconduct.

Argument for loyalty. Instead of substantiating the thesis as true, they tend to accept it by virtue of loyalty, affection, reverence, etc.

Argument for authority. Reference to an authoritative person or collective authority instead of a specific justification for the thesis.

We recommend interesting articles Section Lecture notes, cheat sheets:

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