The method of single similarity refers to. The method of similarity as a method of scientific induction. Elimination induction

Plan

1. The difference between scientific induction and popular induction.

2. The main types of scientific induction.

The difference between scientific induction and popular induction.

Incomplete induction. Popular induction

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

The incompleteness of inductive generalization is expressed in the fact that not all are investigated, but only some elements or parts of a class. Logical passage in incomplete induction from some to all elements or parts of a class is not arbitrary. It is justified on empirical grounds - an objective relationship between universal the nature of the signs and their stable repeatability in experience for a certain kind of phenomena. Hence the widespread use of incomplete induction in practice. So, for example, during the sale of a certain product, they conclude about the demand, market price and other characteristics of a large batch of this product based on the first sample deliveries. In production conditions, according to selected samples, they conclude about the quality of a particular mass product, for example, oil, metal sheet, wire, milk, cereals, flour - in the food industry.

Inductive transition from some NS to all cannot pretend to be a logical necessity, since the repeatability of a feature may be the result of a simple coincidence.

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

On this basis, incomplete induction is referred to believable (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 highly plausible.

Significant influence on the nature of logical following in conclusions; Incomplete induction is provided by the method of selection of the initial material, which manifests itself in the methodical or systematic formation of the premises of inductive inference. According to the selection method, two types of incomplete induction are distinguished: (1) induction by enumeration, named popular induction, and 2) induction by selection, which is called scientific induction.

Popular induction is called generalization, in which, by enumeration, they establish the belonging of a feature to some objects or parts of the class and, on this basis, problematically conclude that it belongs to the entire class.

In the process of centuries of activity, people observe a stable recurrence of many phenomena. On the basis of the emerging generalizations, which are used to explain the occurred and predict future events and phenomena. Such generalizations are associated with observations of the weather, the influence of price on quality, demand for supply. The logical mechanism for most of these generalizations is popular induction. She is sometimes called by induction via simple enumeration.

The recurrence of signs in many cases really reflects the general properties of phenomena. Generalizations built on its basis perform an important function of guiding principles in the practical activities of people. Without such simple generalizations, not a single type of labor activity is possible, be it the improvement of tools, the development of navigation, successful farming, contacts between people in a social environment.

Popular induction determines the first steps in the development of scientific knowledge. Any science begins with empirical research - observation of the corresponding 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 by a simple enumeration of recurring features. They fulfill an important heuristic function initial assumptions, guesses and hypothetical explanations that need further verification and refinement.

A purely enumerative generalization arises already at the level of adaptive-reflex reactions of animals, when repeated stimuli reinforce conditioned reflex... At the level of human consciousness, a repeating feature in homogeneous phenomena does not simply generate a reflex or a psychological sense of expectation, but suggests the fact that repetition is not the result of a purely random combination of circumstances, but the manifestation of some undetected dependencies. The validity of conclusions in popular induction is mainly determined by quantitative indicator: the ratio of the studied subset of objects (sample or sample) to the entire class (population). The closer the studied sample is to the whole class, the more thorough, and therefore, more likely, the inductive generalization will be.

In conditions when only some representatives of the class are investigated, the possibility of erroneous generalization... An example of this is the one obtained using the popular induction and long time, common in Europe generalization "All swans are white." It was built on the basis of numerous observations in the absence of conflicting cases. After landing in Australia in the 17th century. Europeans discovered black swans, generalization was disproved.

Erroneous conclusions about the conclusions of popular induction can appear due to non-compliance with accounting requirements conflicting cases, which make the generalization untenable.

Erroneous inductive conclusions can appear not only as a result of delusion, but also due to unscrupulous, biased generalizations, when contradictory cases are deliberately ignored or hidden.

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

Scientific induction

Scientific induction is called inference, in which generalization is built by selecting necessary and excluding random circumstances.

Depending on the methods of research, there are: (1) induction selection method(selection) and (2) induction by elimination(elimination).

Selection induction

Induction by selection method, or selective induction, 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 a methodical selection of phenomena from different parts of this class.

Concept variety of observation conditions turns out to be very different for specific types of sets. In one case, it takes on the character of spatial species distinction, in the other - temporary, in the third - functional, in the fourth - mixed.

An example of induction by the selection method is the following reasoning about students' knowledge of logic. So, having selected four students from the back rows of 25 students, it can be noted that not one of them had any knowledge. If, on this basis, it is generalized that the whole group has no knowledge of logic, 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 students is not made from the back desks, but taking into account the different location and the presence of an intelligent person. If students are selected from the first and last desks, with and without glasses, then it can be assumed with a high probability that the whole group has great knowledge of such an interesting subject as logic.

A reliable conclusion in this case is unlikely to be justified, since the possibility of ignorance of the subject among students who were not directly questioned is not excluded.

Elimination induction

Induction by the method of exclusion, or eliminative induction, is a system of inference in which conclusions about the causes of the phenomena under study are built by finding confirming circumstances and excluding circumstances that do not satisfy the properties of causation.

The cognitive role of eliminative induction is the analysis of causal relationships. Causal call such a connection between two phenomena, when one of them - the cause - precedes and causes the other - action. The most important properties of the causal relationship, which predetermine the methodical nature of eliminative induction, are its characteristics such as: (1) universality,(2)sequence in time,(3)need and (4) unambiguity.

(1) The universality of causation means that there are no causeless phenomena in the world. Each phenomenon has its own cause, which can be identified earlier or later in the process of research.

(2)Time consistency means that the cause always precedes the action. In some cases, the action follows the cause instantly, in a matter of fractions of a second. For example, a firearm is fired as soon as the primer in the cartridge ignites. In other cases, the cause causes an action over a longer period of time. For example, the demand for a product can change its price over several hours, days, or months, depending on the volume of demand and the elasticity of supply. In the social sphere, causal relationships can take place over many months and years, in geology, over centuries and millennia.

Since the cause always precedes the action, out of many circumstances in the process of inductive research, only those are selected that have manifested earlier the action of interest to us, and excluded from consideration(eliminate) those that arose simultaneously with it and appeared after it.

Consistency in time is a necessary condition for causality, but by itself it is not enough to reveal the real cause. The recognition of this condition as sufficient often leads to an error called "After that, then, because of this"... Determination of the volume of production, for example, tended to be considered the reason for determining the price, because value is perceived later than quantity, although these are simultaneously occurring events.

(3)The causal relationship is distinguished by the property of necessity. This means that an action can be carried out only if there is a reason, the absence of a reason necessarily leads to an absence of action.

(4) Unambiguous nature of causation manifests itself in the fact that each specific cause always causes a completely definite action corresponding to it. The relationship between cause and effect is such that changes in cause necessarily entail changes in action, and conversely, changes in action are indicative of a change in cause.

The noted properties of causal dependence play the role of cognitive principles that rationally guide inductive research and form special methods for establishing causal relationships.

The use of the methods of eliminative induction is associated with a certain coarsening of the real relationships between phenomena, which is expressed in the following assumptions. Each of the circumstances is considered relatively independent and does not interact with others. The highlighted circumstances are considered as a complete list of them, and it is assumed that the researcher has not overlooked other circumstances.

These assumptions, combined with the basic properties of causality, constitute a methodological the basis of the conclusions of eliminative induction, defining the specifics of logical consequence when applying methods of establishing causal relationships.

A great contribution to the development of methods of eliminative induction was made by natural scientists and philosophers: F. Bacon, J. Herschel, J. S. Mill.

Difference between scientific induction and popular induction

The differences are at least based on the principles of organization of the induction data methods. Scientific induction is based on facts that exclude chance and some unverified evidence. Popular induction is inference in which the whole action, class, or nature of something is made only on the basis of any one attribute, incident, or shade of a given class. Simply put, having made a logical process of obtaining a new judgment, a person following popular induction draws a conclusion about the whole system on the basis of one or two facts. That may not always be an objective and comprehensive conclusion and may not always reveal all the nuances, aspects and the entire spectrum of the issue. In principle, we can say that sometimes an erroneous opinion develops, a judgment which can be fundamentally opposite to the truth. And yet scientific induction also does not claim to be the most infallible method. Rather, in order to achieve the truth, one must use a complex of methods and a versatile study of the problem.

Scientific induction methods

Modern logic describes five methods for establishing causal relationships: (1) the method of similarity, (2) the method of difference, (3) the combined method of similarity and difference, (4) the method of concomitant changes, (5) the method of residuals.

Let's consider the logical structure of these methods.

This method is an inference based on comparing several cases of the occurrence of the same phenomenon and identifying the actual cause based on a single similarity. For example, take some phenomenon a and the accompanying circumstances ABC. To use the method of similarity, consider other circumstances when this phenomenon occurred under different and only partially similar circumstances; let's say under the circumstances of AKM. Comparing these cases and relying on the rule of causality, according to which a phenomenon cannot occur in the absence of its cause, we can conclude that the cause a there can be no VS circumstances, since they are absent in the second case, when the phenomenon a happened again. We can say the same about the CM circumstances, since they did not exist in the first case, when the phenomenon a, therefore, it remains to be assumed that the cause a is circumstance A.

If two or more cases of the onset of the observed phenomenon are similar only in one previous circumstance, then this circumstance is probably the cause of this phenomenon:

ABC - a,

AKM - a,

there is probably a reason a.

Using the similarity method to determine the cause of the phenomenon under study, it should be remembered that the cases of this phenomenon were as different as possible from each other in the circumstances; such a selection greatly facilitates the process of finding the cause and reduces the number of cases required for a conclusion. To this we must add that the reasoning that leads us to the conclusion about the cause of the phenomenon under study is valid only when this phenomenon occurs from one cause.

The method of similarity is widely used in everyday life and science only in the first steps of research as a primary assumption. This assumption is then verified and substantiated using more precise methods establishing a causal relationship.

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Study of the discipline for one semester
Day department: lectures - 18, practical lessons - 18, independent work students - 66. Certification: intermediate control (checking homework, testing), test.

Course program
Topic 1. Subject and significance of the science of logic. Formal language and semantic categories (lecture, practical lesson) The process of thinking and forms of thought. The meaning of logic. History l

Test questions
1. What is the subject of formal logic and what is its meaning? 2. What does the generalization of knowledge about individual subjects and their properties and relationships? 3. What is the difference between logical

After studying "Logic", students should
know: - the history of the emergence and stages of development of logic, the essence, content and specifics of logic as a science; - the essence and content of the principles of logic, to

Methodical recommendations for part-time students
Given the distance learning form of students distance learning, you should pay attention to the following guidelines. First, students should be careful to

The laws of logic and the principles of correct thinking
Introduction. general characteristics basic laws of logic. Identity law. The law of contradiction. The law of the excluded third. The law of sufficient reason. Conclusion. Practical ass

Language as a sign system. Sign concept
Introduction. Concept linguistic form... Natural and artificial languages. Functions of natural and artificial languages. The sign system of the language. Name, subject, function. Conclusion. Prak

Main characteristics of signs
Introduction. Definition of the sign and sign system. Types of signs. Three types of iconic relationships. Basic principles of semiotics. Conclusion. Practical task: 1. Indications

General principles of constructing truth tables
Introduction. Interpretation of propositional variables. Tabular definitions of propositional connectives. Logical relationships (in truth and falsity) between formulas. Conclusion. NS

Propositional calculus
Introduction. Propositional logic. The general validity of the propositional calculus. Propositional ligaments. The language of the logic of statements. Conclusion. 1. Write down symbolically high

Concept as a form of thinking. general characteristics
Introduction. Definition of the concept. Classification of signs. Content and scope of the concept. Concept and term. Conclusion. Practical task: 1.Kaki

Logical structure and basic characteristics of the concept
Introduction. Types of concepts. Relationships between concepts. Conclusion. Practical task: 1. Give a complete logical description of the concepts (unit

The meaning of concepts in cognition
Introduction. Concept as a member of a logical connection. Logical errors in concepts. Conclusion. Practical exercise: 1. Give an example of a logical connection

Types of concepts Generalization and limitation of concepts
Introduction. Types of concepts by content. Types of concepts by volume. Generalization of concepts. Limitation of concepts. Conclusion. Practical task: 1.Dayt

Types of relations between concepts in terms of content and volume
Introduction. Relationships between concepts in terms of content. Relationships between concepts in terms of volume. Graphic illustration of the relationship of concepts in terms of volume. Conclusion. Practical task:

Categorical judgments
Introduction. Division of judgments by quantity. Division of judgments by quality. United classification of categorical judgments in the "logical square". Distribution of terms in judgment. Conclusion.

Logical relationships between categorical judgments
Introduction. Incompatibility relationship. Compatibility relationships. Graphical diagram of relations (logical square). The dependence of the truth or falsity of judgments on their relationship. Conclusion.

Complex judgments
Introduction. Characterization of conjunctive, disjunctive, implicative and equivalent judgments. Summary table of the truth (falsity) of these judgments Conclusion. Practical task:

General rules for a simple categorical syllogism
Introduction. Terms rules. Parcel rules. Figure rules. The concept of the modes of figures in the syllogism. Conclusion. Practical task: 1. What

Inductive reasoning
Introduction. Induction concept. Full induction. Incomplete induction. Induction through simple enumeration. Scientific induction. Conclusion. Practical task:

Methods for establishing the causal relationship of phenomena
Introduction. Causal relationship of phenomena. Five methods of establishing a causal relationship. Inferences by analogy. Conclusion. Practical task: 1.O

Hypothesis
Introduction. General characteristics of the hypothesis. Types of hypotheses. Development of the hypothesis. Hypothesis testing. Factual (decisive experience) and logical proof of the hypothesis. Practical task:

Errors in evidence
Introduction. Substitution of a proven thesis. Errors in the grounds of evidence. Errors in the way of proof. Errors of homonymy and amphibole. False follow error. Conclusion. Prak

Logic and language
Language is a sign system, a material form through which people express thoughts. Language has five types: lines, sounds, gestures, color and smell, and three forms: natural, co

The connection between thinking and language
Language and thinking are inextricably linked. With the help of language, we present thoughts in a certain, generally accessible form. This is facilitated by conceptual stereotypes that impose restrictions on and

Logical and psychological
By reasoning logically, we follow the principles and rules that indicate how the "correct" conclusions should be drawn. The principles of logic establish the standards by which we judge the quality of someone

Semantic categories
Logical semantics studies the relationship between sign and meaning, the rules for translating abstract symbols into the language of meaningful knowledge. In logic, it is important to find the compatibility of natural and artificial language

Thought process and thought forms
There are many ways to represent the process of thinking. For a biologist, this is the activation of groups of neurons, for a psychologist, it is a combination of a number of images in the mind, for a cyberneticist, this is a process before

General characteristics of the concept
Logical thinking represents various connections of thoughts. If we look closely at the judgment, we will see that it consists of some thoughts that we repeatedly encountered in other judgments.

Concept and presentation
Every concept is a thought about the attributes of an object. However, not every thought about features is a concept. In sensory cognition, representation is also a thought about the attributes of an object. Submitting an item is

Signs of the concept
Those thoughts that form the integrity of the judgment are called concepts. The thought of an object is a concept only if the thought object has a similarity or difference with other objects, then e

Types of concepts
Any concept has two logical characteristics - content and volume. The essential features of the subject constitute the content of the concept. Meaningless concepts are not

Functions of concepts
Language is a means of thinking. It expresses concepts that serve many functions. The main ones are the following: 1. Symbolic function. The concept becomes symbolic

Self-test questions
1. List the attributes of the subject in the logical classification. 2. What is the difference: a word, a concept, a term? 3. What is the content and scope of the concept? 4. Explain the meaning of the law

Definition of concepts
Definition of concepts (definitio) is one of the most important logical operations that we constantly perform as in Everyday life and in the scientific process. Its meaning is that, revealing

Implicit definitions
If it is impossible to define concepts through generic and specific characteristics, then a description of the relationship between the defined concepts is used. The peculiarity of such definitions is that the subject is determined

Limitation and generalization of concepts
In the process of thinking, it is often necessary to concretize knowledge about the subject of thought. Refining the concept, we introduce new features, thereby increasing its content, but the scope of the concept decreases.

Division of concepts
Objects that are thought of in a concept constitute a well-known set, which includes separate groups of objects. In the process of dividing, we find out which subsets the original set consists of

Self-test questions
1. What is the division of the concept? 2. What is the difference between dichotomous division and species-forming division? 3. What are the principles of classification? 4. What are the functions of the class

General characteristics of the judgment
Judgment is an expanded concept; since a concept contains some features of the object of thought, then a judgment is a form of thought in which the connection between the object of thought and its

Judgment structure
A judgment as a logical form consists of the following elements: subject, predicate and connective. Subject (Latin subjectum - underlying, subject) of the EU

Modality of judgments
The modality of a judgment (lat. Modus - way, measure, mood) expresses the degree of existence, property, relationship, reflected in the judgment. At the same time, in the judgment, the act is approved or denied.

The dependence of the cognitive value of a judgment on its form
The meaning or importance of a judgment for knowledge depends largely on its form. Thus, conditional and separative judgments become valuable for knowledge only in connection with categorical judgments. V

Determine the modality of the judgment. Bring them schemes
Example: A). Ukhta south of Vorkuta. - Judgment about the attitude of the place. xRy = R (x, y). B). There is no smoke without fire. - Judgment of existence. P is. V).

Make diagrams of difficult judgments
Example: Emission is the production and issue of money or securities into circulation. Scheme: S is P (Р¹ Λ Р² V Р³) & nb

Identify three groups of judgments: compatible, incompatible, partially compatible
Example: Not a single hair fell from his head. Many wanted to see him. He lost all his hair. Some nuts have a right hand thread. Everyone came on time.

Tabular definition of the truth (falsity) of complex judgments
We have already said above that a judgment can be classified either as true or as false, but not both together. The "truth" or "falsity" of a declarative sentence that

Self-test questions
1. What is judgment transformation? 2. How is the reversal of judgment different from the reversal of judgment? 3. What principles is the truth (falsity) of a judgment subject to? 4. Kaku

General characteristics of inference
If the main task of logic is to draw up methods for acquiring and proving knowledge, then one of the main methods is inference. Inference is called such a method of thinking.

Direct inferences
We can derive inference from parcels by transforming the latter. The truth of the conclusion in this case depends entirely on the truth of the premises, unless, of course, the transformation rules are violated, which

Syllogism
Syllogism (Greek syllogismos - counting) is a type of inference in which it is required to determine whether a given conclusion follows from two or more judgments. Having recognized the truth of the pos

Entimemes
In the practice of our thinking, both ordinary and scientific, we miss either one of the premises or the conclusion. Such syllogisms, in which one or another part is not expressed explicitly, are called

Conditional syllogisms
If in the syllogism both premises are taken as conditional judgments, then the conclusion will also be a conditional judgment, and the syllogism will be an indirect conditional inference. If A

Exercises
A) Determine the modality of the judgment. Give their schemes. Example: 1). Ukhta south of Vorkuta. - Judgment about the attitude of the place. xRy = R (x, y). 2). No smoke

Exercises
A). Indicate which of the following conclusions were obtained with the help of complete, and which with the help of incomplete induction: 1). All students of our group completed internships. 2). The angle of incidence is equal to the angle of reflection.

Difference method
To make a conclusion using this method, it is necessary to have two cases: a case in which the phenomenon under study occurs, and a case in which it does not occur. Moreover, they are selected so that they are similar

Combined method of similarity and difference
This method combines both preceding rules, so it can be formulated as follows: if two or more cases of the occurrence of the observed phenomenon are similar only in one preceding situation

Method of accompanying changes
The method of concomitant changes is based on the principle of causation, which states that any change in the cause causes a corresponding change in the effect; and vice versa, any change

Residual method
This method is based on the following observation: if a complex phenomenon is the result of a complex cause, then each simple element of this phenomenon is caused by a simple element of a complex cause, corresponding

Self-test questions
What is needed to find the real cause or the real effect? What is the "method of similarity" based on? What is necessary for the inference according to the "method of differences

Exercises
Determine which methods of establishing a causal relationship are applicable, write them down in the form of a diagram and in the form of judgments that form a causal relationship. Potatoes sprouted in a dark pog

Similar inferences
Inference by analogy (Greek analogia - similarity, similarity) refers to a modification of the traductive type of inference. The only difference is that the basis of traduction is identity, mouth

Exercises
Determine the type of analogy, write them down in the form of a diagram and in the form of judgments that form a connection between objects or relationships. Example: When exploring rocks in Av

Evidence concept
The connection between concepts and judgments that we use to express thoughts is a reflection of the connection between objects, their signs, their relationships and their laws. But the truth of the judgments is not about

Exercises
Highlight the thesis and arguments. Choose one of the inference forms and build a demo. Example: Student Petrov passed his thesis project ahead of schedule, because he

Proof and rebuttal rules
In the process of proof, errors are possible that arise in the case of intentional or not intentional violation of the rules. The rules of proof are divided into three groups according to the structure of the proof:

Types of evidence
According to the purpose, the proofs are divided into: 1) proof of the truth of the thesis and 2) proof of the falsity of the thesis. The first, aimed at establishing the truth of the thesis, is called pro

Self-test questions
1. What three groups of rules in the proof do you know? 2. What explains the clarity and clarity in the formulation of the thesis? 3. What is a "thesis substitution"? 4 why the argument is true

Exercises
Pick up the arguments and build a direct proof of the thesis. Example: Student Ivanov was summoned to the court to testify. Arguments

The concept of a hypothesis and the conditions for its appearance
The word hypothesis (Greek hypothesis - assumption) has several meanings. Firstly, this is a guess about a fact that is not yet available for detection, but can manifest itself with a probability close to

Constructing a hypothesis
Constructing a hypothesis is a complex logical process involving various forms of inference. In some cases, a hypothesis arises as a result of comparing two single phenomena, i.e. it is based on

Hypothesis development
A hypothesis is not reduced to putting forward an assumption, but goes through a development process, during which it is corrected, supplemented with new assumptions, and either refuted and replaced.

Confirmation of the hypothesis
In order to turn into valid knowledge, the assumption is subject to scientific and practical verification. Hypothesis Testing Process Using Various Logical Techniques

Exercises
Pick up the facts and build a hypothesis. Example: In the well-known film "Sannikov Land" it was suggested that in the Northern Arctic

Identity law
It should be noted that any correct thought must be definite. This means that in the process of reasoning, one cannot substitute one object of thought for another. For example, in the argument “life is in full swing

The law of contradiction
From the law of identity it follows that no thought can be identical to the thought that denies it, that is, in order to be understood, it is necessary to comply with the requirement of consistency of thought

The excluded third law
The fact that a thought can be equated either with truth or with a lie follows from the law of the excluded third: of two mutually denying judgments, one is certainly true at a given time, in a given place

The law of sufficient reason
The correctness or truthfulness of thought is due to a sufficient basis for them. Indeed, we can consider this or that thought to be true only after the grounds are given, which are already about

Self-test questions
1. What are called the laws of thinking? 2. Why are the laws of thinking called formal laws? 3. How is the law of identity formulated? 4. How the law of contradiction is formulated

Exercises
Determine which logical law requirement is violated in the following reasoning. Example: This student did not reveal the main content of the topic, but deserved

Basic logical concepts
AXIOM (gr. Axioma - meaningful, worthy of respect, indisputable) is a true judgment, which, in the deductive construction of any theory, is accepted without evidence as a quality and

Shape rules
No. Figure Correct modes

Terms rules
No. Rule Example of an error Notes There should be only three terms in the syllogism Movement -

Parcel rules
No. Rule Example of an error Remarks Two negative premises cannot be

Logical symbols
Title Image Ordinary language Formula (diagram) how to spell

In relation to the thesis
Error rules 1. The thesis must be clear and precise 1. Putting forward an unclear, imprecise thesis 2. The thesis must

Glossary
LAW OF LOGIC - stable, essential, repetitive connection of thoughts; possesses the following properties: a) certainty (representation of an object in the same features); b) last

This method is as follows. Let's say we are looking for the cause of some phenomenon a. We know from observation that the phenomenon of a masses takes place under the circumstances of ABC. Circumstance ABC is complex, it is a collection of different parts (elements): A, B, C. What part (element) of this complex circumstance (A or B, or C) is the cause of the phenomenon a by observing only one case of connection a with the circumstance ABC cannot be said. Then we set ourselves the task of finding several cases when the phenomenon a exists. Observing, we establish that the phenomenon of a mass takes place also under the circumstances of AD and under the circumstances of AFD *

Comparing these three cases, we find that the phenomenon a takes place under circumstances (ABC, ADE, AFG), which are different in everything and only in one thing are similar - they all have the same circumstance A, since circumstances B, C, D , E, F, G cannot be the cause of a, since the phenomenon a occurs even in the absence of any of these circumstances, it is concluded that the cause of the phenomenon a is the only circumstance A that is similar in all cases.

The inference based on the method of single similarity can be written in the form of the following diagram:

Example. In one regional communications office, there were three cases of theft in the same way (valuables were taken out of insurance bags without damaging them): on August 4, December 20 and 25. The investigation established that in all three cases the mail was transported from one communications office to the second by Sasha's cab. In all three cases, different persons sent and received mail on August 4 - Petrenko and Ivanenko, on December 20 - Nikolayenko and Yakovenko, on December 25 - Vorona and Savchenko. On this basis, the investigator put forward a version that the theft was committed by the cabman Sashin.

In the form of a diagram, this conclusion can be written as follows:

The application of the single similarity method consists of three sequential steps.

1. First of all, all those cases are established where there is a phenomenon and the cause of which we find out.

2. Then each case is analyzed and the circumstances under which the phenomenon a occurs are highlighted.

3. After that, the circumstances common to all these cases are sought, which are the cause of the phenomenon and what interests us.

The conclusion based on the method of single similarity is based on the following rule: if two or more cases of the phenomenon under study have only one circumstance in common, and all other circumstances are different, then this single similar circumstance is the cause of this phenomenon.

The method of single similarity gives conclusions that are not reliable, but probable. The likelihood of incarceration depends on different conditions: a) on the number of cases under consideration. The more cases investigated, the more likely the conclusion will be; b) from the depth and thoroughness of the study of all circumstances, from the accuracy of establishing what in all cases is similar to only one furnished; c) the degree of probability of a conclusion by the method of a single similarity depends only on how significant the differences are in all circumstances, except for the only similar one, which we define as the cause. The more differences in circumstances, the more likely it will be to conclude that the cause of the phenomenon that interests us is the circumstance that alone turned out to be the same in all cases.

In inferences based on the method of single similarity, one should also keep in mind the rates. In some cases, it may be that the only similar circumstance is taken as the cause is itself complex and the reason for the phenomenon under study is not the entire circumstance, but only some of its part, which must be determined. In other cases, it may turn out that the circumstance taken as a cause does not act by itself, but together with others, that is, only a part of the cause or one of the reasons, and we incorrectly considered it to be the only reason.

The method of a single similarity is often used in investigative practice to put forward versions of a case.

1. Method of similarity

According to the method of similarity, several cases are compared, in each of which the phenomenon under study occurs; however, all cases are similar in one and different in all other circumstances.

The method of similarity is called the method of finding commonality in the different, since all cases differ markedly from each other, except for one circumstance.

The logical mechanism of inductive inference by the method of similarity presupposes a number of cognitive prerequisites.

(1) Requires general knowledge of possible reasons ah investigated phenomenon.

(2) All circumstances that are not necessary for the investigated action and thus do not satisfy the basic property of causality must be excluded (eliminated) from the preceding ones.

(3) Among the many previous circumstances, there are similar and recurring circumstances in each of the considered cases, which will be the probable cause of the phenomenon.

In general, the logical mechanism inductive method similarity takes the form of deductive reasoning in the tollendo ponens modus of separative-categorical inference.

The validity of the conclusion obtained using the method of similarity depends on the number of cases considered and the variety of observation conditions. The more cases are investigated and the more varied the circumstances among which a similar one is found, the more solid the inductive inference and the higher the degree of probability of the conclusion. The incomplete induction characteristic of the incomplete experience is manifested in the fact that observation and experiment do not guarantee an accurate and complete knowledge of the previous circumstances, among which the search for a possible cause is taking place.

Despite the problematic nature of the conclusion, the method of similarity 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.

A reliable conclusion can be obtained by the method of similarity only if the researcher knows exactly all the antecedent circumstances that constitute a closed set of possible causes, and also knows that each of the circumstances does not interact with others. In this case, inductive reasoning acquires a demonstrative value.

2. Difference method

According to the method of difference, two cases are compared, in one of which the phenomenon under investigation occurs, and in the other it does not occur; the second case differs from the first in only one circumstance, while all the 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 distinction is used both in the process of observing phenomena in natural conditions, and in the conditions of a laboratory or industrial experiment. In the history of economics, many laws were discovered by the method of difference (the law of diminishing marginal utility). In agricultural production, this method is used to check, for example, the effectiveness of fertilizers.

Difference reasoning also presupposes a number of premises.

(1) A general knowledge of the antecedent circumstances is required, each of which may be the cause of the phenomenon under investigation.

(2) From the members of the disjunction it is necessary to exclude circumstances that do not satisfy the condition of sufficiency for the investigated action.

(3) Among the many possible causes, only one circumstance remains, which is considered as a real cause.

The logical mechanism of inference by the method of difference also takes the form of the modus tollendo ponens of divisional-categorical inference.

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

Since in the conditions of empirical knowledge it is difficult to pretend to be an exhaustive statement of all the circumstances, conclusions based on the method of difference in most cases give only problematic conclusions.

According to many researchers, the most plausible inductive conclusions are reached by the difference method.

3. The combined method of similarity and difference

This method is a combination of the first two methods, when, by analyzing many cases, both similar in different and different in similar are found.

As an example, let us dwell on the above reasoning by the method of similarity about the causes of the disease of three students. If we supplement this reasoning with an analysis of three new cases in which the same circumstances are repeated, except for the similar, i.e. the same foods were consumed, except for beer, and no disease was observed, then the withdrawal will proceed in the form of a combined method.

The likelihood of a conclusion in such a complicated reasoning increases markedly, because the advantages of the method of similarity and the method of difference are combined, each of which separately gives less reliable results.