Chapter V. Induction Another, besides deduction, the most general type of inference is induction. It contains a deep originality, and it is in close relationship with deduction. In the real practice of thinking, its essence also manifests itself in diverse

2. Complete induction Complete induction is obtained if, firstly, all elements of the class of objects are examined and, secondly, if it is established that each of them belongs (or does not belong) to the same general property (relationship) .In the simplest case it looks like

3. Incomplete induction Incomplete induction is an inference about the entire class of objects as a whole based on the study of only part of the objects of this class. Incomplete induction formula: S1 - PS2 - P…..Sn - PS1, S2 ... Sn ... form part of the class S. Therefore, all S are R.B

Chapter V. Induction 1. Induction as a type of inference Express the structure of the following inductive inferences in schematic form and determine the nature of the conclusion: “Take, for example, Roger Bacon's study of the origin of the colors of the rainbow. At first he seems to have

1. Induction as a type of inference Express the structure of the following inductive inferences in schematic form and determine the nature of the conclusion: “Take, for example, Roger Bacon's study of the origin of the colors of the rainbow. At first, it seems, he had the idea of ​​tying

§ 3. SCIENTIFIC INDUCTION Scientific induction is an inference in which a generalization is constructed by selecting the necessary and excluding random circumstances. Depending on the methods of research, they distinguish: (1) induction by the method of selection (selection) and (2) induction by the method

3.13. What is induction? Recall that indirect inferences are divided into deductive, inductive and analogical inferences. Deductive inferences, or syllogisms, the varieties of which we discussed above, provide reliable conclusions. Inductive inference

Part Two The popular “American Dream”: the mirage of luxurious happiness Since the expression “American Dream” is widely used today in intellectual and popular culture (here we mean “culture” in the American, and not in the Russian “higher” sense), in

INTRODUCTION

Scientific induction is an inference in which, based on the knowledge of the necessary characteristics or the necessary connection of a part of the objects of a class, a general conclusion is made about all the objects of the class.

Scientific induction, like complete induction and mathematical induction, produces a valid conclusion. The reliability (and not the probability) of the conclusions of scientific induction, although it does not cover all the objects of the class being studied, but only a part of them (and a small one at that), is explained by the fact that the most important of the necessary connections is taken into account - the causal connection.

The use of scientific induction made it possible to formulate general judgments and scientific laws (physical laws of Archimedes, Kepler, Ohm, etc.). Thus, Archimedes' law describes the property of any liquid to exert upward pressure on a body immersed in it.

Using scientific induction, the laws of social development were obtained.

A clear fixation of the significant differences between the classical and modern understanding of induction is necessary, which is important for solving such questions of methodology as induction and the problem of discovering scientific laws, induction and its role in life, etc.

INCOMPLETE INDUCTION. POPULAR INDUCTION

Incomplete induction is an inference in which, based on the attribute’s belonging 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, but only some elements or parts of the class are studied. 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 - the objective dependence between the universal nature of 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 selective deliveries. In production conditions, based on selective samples, conclusions are drawn about the quality of one or another mass product, for example, oil, metal sheets, wire, milk, cereals, flour - in the food industry.

The inductive transition from some to all cannot claim logical necessity, since the repeatability 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. In this case, the discovery of at least one case that contradicts the generalization makes the inductive conclusion untenable.

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

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

Popular induction is a generalization in which, by 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 centuries-old activity, people observe a stable repetition of many phenomena. On this basis, generalizations arise that are used to explain current and predict future events and phenomena. Such generalizations are associated with observations of the weather, the influence of price on quality, and demand on supply. The logical mechanism for most such generalizations is popular induction. It is sometimes called induction through simple enumeration.

The repeatability of signs in many cases actually reflects the universal 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 work activity is possible, be it the improvement of tools, the development of navigation, successful farming, or 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 relevant objects in order to describe, classify, identify stable connections, relationships and dependencies. The first generalizations in science are due to the simplest inductive conclusions through a simple listing of repeating features. They perform an important heuristic function of initial assumptions, guesses and hypothetical explanations that need further verification and clarification.

A purely enumerative generalization arises already at the level of adaptive reflex reactions of animals, when repeated stimulation reinforces the conditioned reflex. At the level of human consciousness, a repeating sign in homogeneous phenomena does not simply generate a reflex or a psychological feeling of expectation, but suggests that repeatability is not the result of a purely random coincidence, but a manifestation of some unidentified dependencies. The validity of conclusions in popular induction is determined mainly by a 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 where only some representatives of a class are studied, the possibility of erroneous generalization cannot be excluded. An example of this is the generalization All swans are white, which was obtained using popular induction and existed for a long time in Europe. It was built on the basis of numerous observations in the absence of contradictory cases. After those who landed in Australia in the 17th century. Europeans discovered black swans, the generalization was refuted.

Erroneous conclusions about the conclusions of popular induction may arise due to failure to take into account the contradictory cases that make the generalization untenable.

Erroneous inductive conclusions can arise not only as a result of delusion, but also from dishonest, biased generalizations, when contradictory cases are deliberately ignored or hidden.

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

Exercises

1. Establish by what method of scientific induction the following was obtained

generalization:

As a result of three checks of student attendance at lectures under different circumstances, the result was:

Conclusion: The first pair (S) is the cause of poor attendance (P). First check was on first couple on Saturday, the first week of school. Second the test took place in the second week of school, on first couple on Wednesday. Third the test took place in the third school week, on Thursday, on the first couple.

Conclusion: in all three cases of verification, the common circumstance is – first pair.

2. Use inductive reasoning and answer the question: “Which famous director did not star in his own films: N. Mikhalkov, G. Danelia, E. Ryazanov, A. Tarkovsky?” What kind of induction are we talking about?

3. Give an example of a correct deductive inference.

The difference between scientific induction and popular induction

The differences, at a minimum, are based on the principles of organization of inductive data methods. Scientific induction is based on facts that exclude chance and some unverified data. Popular induction is an inference in which a whole action, class, or nature of something is inferred from just one characteristic, incident, or shade of that class. Simply put, having made the logical process of obtaining a new judgment, a person who has followed popular induction draws a conclusion about the entire system on the basis of one or two facts. Which may not always be an objective and comprehensive conclusion and may not always reveal all the nuances, sides and the entire spectrum of this issue. In principle, we can say that sometimes an erroneous opinion is formed, a judgment that can be radically opposite to the truth. Nevertheless, scientific induction also does not claim to be the most error-free method. Rather, in order to achieve the truth, one must use a set of methods and a comprehensive study of the problem...

Incomplete induction. Popular induction

Incomplete induction is an inference in which, based on the attribute’s belonging 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 everything is studied, but only some elements or parts of a class. Logical transition in incomplete induction from some to all elements or parts of a class is not arbitrary. It is justified by empirical grounds - the objective dependence between universal the nature of the signs and their stability 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 selective deliveries. In production conditions, based on selective samples, conclusions are drawn about the quality of one or another mass product, for example, oil, metal sheets, wire, milk, cereals, flour - in the food industry.

Inductive transition from some co everyone cannot claim logical necessity, since the repeatability of a feature may be the result of a simple coincidence.

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

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

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

Popular induction is a generalization in which, by 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 centuries-old activity, people observe a stable repetition of many phenomena. On this basis, generalizations arise that are used to explain current and predict future events and phenomena. Such generalizations are associated with observations of the weather, the influence of price on quality, and demand on supply. The logical mechanism for most such generalizations is popular induction. She is sometimes called by induction via simple enumeration.

The repeatability of signs in many cases actually reflects the universal 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 work activity is possible, be it the improvement of tools, the development of navigation, successful farming, or 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 relevant objects in order to describe, classify, identify stable connections, relationships and dependencies. The first generalizations in science are due to the simplest inductive conclusions through a simple listing of repeating features. They perform an important heuristic function initial assumptions, conjectures and hypothetical explanations that need further verification and clarification.

A purely enumerative generalization arises already at the level of adaptive reflex reactions of animals, when repeated stimulation reinforces the conditioned reflex. At the level of human consciousness, a repeating sign in homogeneous phenomena not only gives rise to a reflex or a psychological feeling of expectation, but suggests that repeatability is not the result of a purely random coincidence, but a manifestation of some unidentified dependencies. The validity of conclusions in popular induction is determined mainly quantitative indicator: the ratio of the studied subset of objects (sample or selection) 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 where only some representatives of the class are studied, the possibility cannot be excluded erroneous generalization. An example of this is the generalization “All swans are white,” obtained using popular induction and existing for a long time in Europe. It was built on the basis of numerous observations in the absence of contradictory cases. After those who landed in Australia in the 17th century. Europeans discovered black swans, the generalization was refuted.

Erroneous conclusions about the findings of popular induction may arise due to failure to comply with accounting requirements contradictory cases which make the generalization untenable.

Erroneous inductive conclusions can arise not only as a result of delusion, but also from dishonest, biased generalizations, when contradictory cases are deliberately ignored or hidden.

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

Scientific induction

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

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

Induction by selection

Induction by the method of selection, or selective induction, is an inference in which the conclusion about the membership of a characteristic in a class (set) is based on knowledge about a sample (subset) obtained by methodically selecting phenomena from various 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 a spatial difference, in another - temporary, in the third - functional, in the fourth - mixed.

An example of induction using the selection method is the following reasoning about students’ knowledge of logic. So, having selected four students from the back rows out of 25 students, it can be noted that not one of them has any knowledge. If we make the generalization on this basis that the whole group has no knowledge of logic, then it is obvious that such a popular induction will give an unlikely conclusion.

It’s a different matter if the choice of the same number of students is made not from the back desks, but taking into account different locations and the presence of an intelligent person. If students from the first and last desks, with and without glasses, are selected, it means that it can be assumed with high probability that the entire 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 interviewed cannot be ruled out.

Induction by 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 identifying 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 they call such a connection between two phenomena when one of them - the cause - precedes and causes the other - action. The most important properties of a causal relationship that predetermine the methodological nature of eliminative induction are its characteristics such as: (1) universality, (2) sequence in time (3) necessity and (4) unambiguity.

(1) 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 during the research process.

(2)Sequence in time means that cause always precedes effect. In some cases, the action follows the cause instantly, in a matter of seconds. For example, a firearm is fired immediately as soon as the primer in the cartridge ignites. In other cases, the cause causes the effect after a longer period of time. For example, the demand for a product may change its price after a few hours, days, or months, depending on the quantity demanded and the elasticity of supply. In the social sphere, causal connections can take place over many months and years, in geology - over centuries and millennia.

Since cause always precedes action, from many circumstances in the process of inductive research only those that manifest themselves are selected earlier the action we are interested in, and excluded from consideration(eliminate) those that arose simultaneously with it and those that appeared after it.

Sequence in time is a necessary condition for causation, but by itself it is not sufficient to discover the actual cause. Recognizing this condition as sufficient often leads to an error called “after this, therefore, because of this”. Determination of production volume, for example, was previously considered to be the reason for determining price, because value is perceived later than quantity, although these are simultaneous events.

(3)Causality is distinguished by the property of necessity. This means that an action can only occur if there is a cause; the absence of a cause necessarily leads to the absence of an action.

(4) The unambiguous nature of the causal relationship manifests itself in the fact that each specific cause always causes a very specific action corresponding to it. The relationship between cause and effect is such that modifications in the cause necessarily entail modifications in the action, and vice versa, changes in the action serve as an indicator of changes in the 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 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 The identified 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 the causal relationship, constitute a methodological the basis of the conclusions of eliminative induction, determining the specifics of logical consequence when applying methods for 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.

Methods of scientific induction

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 look at the logical structure of these methods.

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 finding method common in different, for all the cases differ markedly from each other, except in one circumstance.

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

(1) Requires general knowledge about the possible causes of the phenomenon under study..

(2) Of the previous ones there must be all circumstances that are not necessary for the action under study are excluded (eliminated) and thus not satisfying the basic property of causality.

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

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

The validity of the conclusion obtained using the similarity method depends on the number of cases considered and the variety of observation conditions. The more cases are studied and the more varied the circumstances among which similarities occur, the more thorough the inductive conclusion and the higher the degree of probability of the conclusion. The incompleteness of experience characteristic of incomplete induction is manifested in the fact that observation and experiment do not guarantee accurate and complete knowledge of the preceding circumstances, among which a search for a possible cause is taking place.

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 testing of which leads to the discovery of new truths in science.

Reliable conclusion can be obtained using the similarity method only if the researcher knows exactly all previous circumstances which constitute a closed a bunch of possible reasons, and it is also known that each of the circumstances does not interact with others. In this case, inductive reasoning takes on demonstrative significance.

Difference method

Using 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 in only one circumstance, and all others are similar.

The method of difference is called the method of finding different in similar, for the cases being compared 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 laboratory or industrial experiment conditions. 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.

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

(1) Required general knowledge of previous circumstances, each of which may be the cause of the phenomenon under study.

(2) From the members of the disjunction, circumstances that do not satisfy the condition should be excluded sufficiency for the action under study.

(3) Among the many possible reasons remains the only circumstance which is considered as a valid reason.

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

Reasoning by the method of difference acquires evidential knowledge only if there is accurate and complete knowledge of the antecedent circumstances that make up the closed disjunctive set.

Since in the conditions of empirical knowledge it is difficult to claim an exhaustive statement of all circumstances, conclusions using the method of difference in most cases provide only problematic conclusions.

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

United method of similarities and differences

This method is a combination of the first two methods, when, through analysis of many cases, it is discovered both similar in different, and different in similar.

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

The probability 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.

Concomitant Change Method

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.

Previous inductive methods were based on repetition or the absence of a certain circumstance. However, not all causally related phenomena allow the neutralization or replacement of individual factors that make them up. For example, when studying the influence of demand on supply, it is impossible in principle to exclude demand itself. In the same way, by determining the influence of the Moon on the magnitude of sea tides, it is impossible to change the mass of the Moon.

The only way to detect causal relationships in such conditions is to record them during observation. accompanying changes in previous and subsequent events. The cause in this case is a preceding circumstance, the intensity or degree of change of which coincides with the change in the action under study.

The use of the accompanying change method also requires compliance with a number of conditions:

(1) Knowledge of everyone possible causes of the phenomenon under study.

(2) From the given circumstances there must be eliminated those that do not satisfy the property of unambiguous causality.

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

Associated changes may be straight And reverse. Direct dependency means: the more intense the manifestation of the preceding factor, the more actively the phenomenon under study 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 demand for a product, supply increases; with a decrease in demand, supply decreases accordingly. In the same way, with the strengthening or weakening of solar activity, the level of radiation in terrestrial conditions increases or decreases accordingly.

Inverse relationship is expressed in that the intense manifestation of a previous circumstance slows down activity or reduces the degree of change in the phenomenon under study. For example, the greater the supply, the lower the cost of production, or the higher labor productivity, the lower the cost of production.

The logical mechanism of inductive generalization using the method of accompanying changes takes the form of deductive reasoning in the tollendo ponens mode of dividing-categorical inference.

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

As the number of cases compared that demonstrate concomitant changes increases, the likelihood of a conclusion increases. If the set of alternative circumstances does not exhaust all possible causes and is not closed, then the conclusion in the conclusion is problematic and not reliable.

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

Reasoning using the method of concomitant changes is used to identify not only causal ones, but also others, for example functional connections, when a relationship is established between the quantitative characteristics of two phenomena. In this case, it becomes important to take into account the characteristics characteristic of each type of phenomenon. change intensity scales, within which quantitative changes do not change the quality of the phenomenon. In any case, quantitative changes have lower and upper limits, which are called limits of intensity. In these border zones, the qualitative characteristics of the phenomenon change and thus deviations can be detected when applying the method of accompanying changes.

For example, a decrease in the price of a product when demand falls decreases up to a certain point, and then the price increases with a further drop in demand. Another example: medicine is well aware of the medicinal properties of drugs containing poisons in small doses. As the dose increases, the usefulness of the drug increases only up to a certain limit. Beyond the intensity scale, the drug acts in the opposite direction and becomes hazardous to health.

Any process of quantitative change has its own critical points, which should be taken into account when applying the method of concomitant changes, which effectively operates only within the framework of the intensity scale. Using the method without taking into account the boundary zones of quantitative changes can lead to logically incorrect results.

Residual method

Application of the method is associated with establishing 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.

Using the residue method, a conclusion was made about the existence of certain chemical elements - helium, rubidium, etc. The assumption was based on the results obtained in the process of spectral analysis: new lines were discovered that did not belong to any of the already known chemical elements.

Like other inductive conclusions, the residual method usually gives problematic knowledge. The degree of probability of the conclusion in such a conclusion is determined, firstly, by the accuracy of knowledge about previous circumstances, among which the search for the cause of the phenomenon under study is being carried out, 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 representation of the influence of each of the known causes on the cumulative effect, can lead to the fact that at the conclusion of the conclusion, not a necessary, but only an accompanying circumstance will be presented as an unknown cause.

Reasoning using the residual method is often used in the process of investigating crimes, mainly in cases where an obvious disproportion between the causes and the actions under study. If an action in its volume, scale or intensity does not correspond to a known cause, then the question is raised about the existence of some other circumstances.

The considered methods for establishing causal relationships in their logical structure relate to complex reasoning, in which inductive generalizations are built with the participation of deductive conclusions. Based on the properties of causality, deduction acts as a logical means of elimination(exceptions) of random circumstances, thereby it logically corrects and guides inductive generalization.

Incomplete induction

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 is called incomplete induction.

Scheme of inferences of incomplete induction:

A 1 has the trait R A 2 has the trait R

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

A p has the trait R

A 1 , A 2, ..., A n, - some representatives of the class TO

Apparently every element of the class TO has the trait R

For example, observing the regular alternation of day and night, they conclude that this alternation will take place tomorrow, and the day after tomorrow, etc., i.e. as long as the solar system exists.

The incompleteness of inductive generalization is expressed in the fact that not everything is studied, but only some elements, or parts of a class.

The logical transition in incomplete induction from some elements to all elements or parts is not arbitrary. It is justified by empirical justifications, namely the objective relationship between the universal nature of signs and their stable repeatability in practice for a certain class of phenomena. Hence the widespread use of incomplete induction in practice. Thus, during the sale of a certain product, a conclusion is made about the demand, market price and other characteristics of a large batch of this product based on the first selective deliveries. In production conditions, based on selective samples, conclusions are drawn about the quality of one or another mass product, for example oil, metal, milk, bread, etc.

Inductive transition from some co all class elements cannot claim logical necessity, since repeatability may be the result of a simple coincidence, thus conclusions based on incomplete induction are characterized weakened logical consequence– true premises allow us to obtain not a reliable, but only a probable conclusion. In this case, the discovery of at least one case that contradicts the generalization makes the inductive conclusion untenable.

The probability of a conclusion in this scheme, therefore, can range from very insignificant to almost complete certainty.

Due to this fact, inductive logic develops special methods for assessing the probability of conclusions.

A significant influence on the nature of the logical consequence in the conclusions of incomplete induction is exerted by the method of selecting the source material, which manifests itself in the methodical and systematic formation of the premises of the inductive inference.

Features of incomplete induction: a) used in the study of open classes with an indefinite or infinite number of elements, as well as closed classes, where there is no need to study each element; b) the conclusion is probabilistic in nature and cannot serve as a basis in evidentiary reasoning.

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

Types of incomplete induction

Incomplete induction is divided into two types:

• 1) popular (induction through a simple enumeration, in the absence of a contradictory case);
• 2) scientific induction (the transition to general knowledge is made on the basis of identifying the necessary features and necessary connections between objects and phenomena of nature and society).

Popular induction

Popular induction (induction through simple enumeration) is an inference in which, based on the repeatability of the same feature in a number of homogeneous objects and the absence of a case contradicting this repeatability, a general conclusion is made about the belonging of the feature in question to all objects of this class.

For example, B. Russell has such a parable. A chicken lives in a chicken coop. Every day the owner comes and brings her some grains to eat. The chicken naturally concludes from this that the appearance of the owner is associated with the appearance of grains. But then one day the owner appears not with a grain, but with a knife. This is a contradictory case.

Based on popular induction, many signs, proverbs and sayings have been formulated in the mass consciousness, for example: “Take care of your dress again, but take care of your honor from a young age,” “An old friend is better than two new ones,” etc.

Features of popular induction: a) random or almost random selection of examples; b) insufficient attention to counterexamples; c) cause-and-effect relationships between phenomena are not taken into account; d) the validity of the conclusions is determined mainly by a quantitative indicator - the ratio of the studied subset and the entire class of objects.

Efficiency popular induction largely depends on the extent to which the cases enshrined in the premises will be as numerous as possible; varied; typical.

Popular induction defines the first steps in the development of scientific knowledge. Any science begins its theoretical constructions with empirical research - observations of relevant objects in order to describe, classify, and identify stable connections and dependencies. The first generalizations in any science are made on the basis of the simplest inductive conclusions by simply listing repeating features. They perform the most important heuristic function initial proposals, guesses and hypothetical explanations that need further verification and clarification.

The main value of popular induction is that it is one of the effective means of common sense and provides answers to many life situations in cases where the use of science is not necessary. Based on popular induction, many proverbs and sayings have been formulated in the mass consciousness, for example, “Living life is not a field to cross,” “Small is the spool, but expensive,” “He who does not take risks, does not win,” and others.

As can be seen from these examples, popular induction in an implicit form, it often formulates the rules of behavior, the foundations for constructing a person’s life concept.

For example, the great Russian singer Claudia Ivanovna Shulzhenko often told a parable, the essence of which was to reveal the patterns of human life. “In one of the villages there lived a man. In his youth he was very poor, and he had a large family, and all seven children were daughters, who in the old days faced the prospect of remaining old maids if their father did not give them a dowry. This man decided take his own life. He took the rope and went into the forest, and Death met him. She said: “I know your trouble, but I will help you. You will treat people, and fame and money will come to you." The man answers her: "How can I treat people if I have never done this, and everyone in the area knows about it?!" Death replies: "I will give you advice, just follow it strictly. When you are invited to visit a sick person, you enter the hut and immediately look into the dark corner. If I’m already standing there with a scythe, then say that you were invited late, you can’t help. If I am not there, then give the patient regular tea and he will recover. But remember one single rule that applies to you: “I always come when I’m not expected.”

The fame of the new doctor spread throughout the area and brought him wealth and happiness to his daughters. Many years passed, it was spring again, a man was walking through the forest, in a great mood, and Death met him. He says to her: “Why did you come, I didn’t call you?!”, and she answered him: “In the bustle of life, you forgot my rule that I always come when I’m not expected! I came for you!”

The rule that Death formulated serves as a counterexample in this example of popular induction, which says that no matter how much you give a person tea, if Death comes, it will not help him.

This suggests that the conclusion of popular induction is not certain to be true, but only conjectural, probable, or plausible.

The prevalence of this kind of inference is associated with the natural human tendency to look for examples that confirm judgments that we are predisposed to accept as true.

Popular induction serves as the basis for our faith in the predictions of astrologers and the miracles of psychics. People who want to believe in “miracles”, among the numerous cases of “treatment”, pay attention to what confirms their belief, i.e. take into account examples and ignore counterexamples. Astrologers, soothsayers, fortune tellers, clairvoyants, “hereditary healers” strive to make as many “predictions” as possible so that something predicted comes true, unmistakably counting on the fact that the public will take into account precisely these cases that confirm their predictions and will not reverse attention to unfulfilled predictions.

Popular induction is not a reliable way to justify the correctness of inferences for the following reasons.

• 1. The random nature of the selection of objects belonging to the set A 1 of interest to us makes it possible that the studied subset A possesses this feature, while there are other subsets, for example A 2, A 3,..., that do not possess this feature.
• 2. A simple listing of randomly selected objects may not take into account any type of objects that do not have the characteristic attributed to the objects of a given set in an inductive generalization and, therefore, does not guarantee the absence of a counterexample.

For example, 1 is a prime number; 2 – prime number; 3 is a prime number. 1, 2, 3 are natural numbers. Therefore, all natural numbers are prime.

In this case an error has been made hasty generalizations, when the study of the first three cases is considered a sufficient basis for the formation of an inductive generalization relating to the entire class of natural numbers.

This kind of mistake is especially common in life, when people judge an entire class of objects based on one or two cases. Thus, in social psychology, when analyzing the problem of forming a first impression of a stranger, it is noted that we usually set or follow certain schemes for forming a person’s image, and that each of the schemes is determined by a certain factor. For example, people also tend to overestimate an outwardly attractive person based on other social and psychological parameters that are important to them, such as happiness in family life, luck, high social status, etc., but in practice this is not always true and often acquaintance with these people in life, or reading their published biographies, memoirs, diaries refutes this scheme. This fact has been confirmed in psychology and experimentally. Thus, in the experiments of the famous Russian psychologist A. A. Bodalev, for example, it was shown that the people tested were rated as more beautiful in photographs as more self-confident, happy, sincere, successful, etc.

The considered disadvantages of popular induction show three ways to increase the reliability of conclusions:

• 1) increasing the number of cases studied;
• 2) increasing the diversity of cases considered;
• 3) taking into account the nature of the connection between the objects under consideration and their characteristics; it is desirable that the characteristic be closely related to the essence of the object.

The likelihood of reaching a conclusion based on popular induction will increase significantly if we do not make the following logical errors.

1. Hasty generalization– a logical error consisting in the fact that an inductive generalization is formed on the basis of a few, randomly encountered examples.

This logical error underlies many rumors, conjectures, and immature judgments.

For example, V. Minto in his book “Deductive and Inductive Logic” gives an example of the treatment of wounds in medieval England. A certain Canelm Digley invented an “unction of honor”, ​​which was applied not to the wound, but to the weapon that caused the wound. It was observed that many people were cured in a similar way. On this basis, the author concluded that such treatment is superior in its effectiveness to all other methods of treatment.

2. After this, it means because of this– a logical error consisting in the fact that a simple sequence of events in time is taken for their causal relationship.

This error underlies numerous superstitions that easily arise as a result of connections in time of two events that are in no way connected with each other.

For example, N. G. Chernyshevsky in his work “On Superstitions” described one of the manifestations of this error. The ancient Romans, preparing for battle, noticed that a crow was cawing to the left, and they won. On this basis, the conclusion was made: victory or defeat is determined by which side the crow caws before the battle.

• 3. Replacing the conditional with the unconditional. This logical error lies in the fact that the following is not taken into account: every truth is manifested in a certain combination of conditions, the change of which can affect the truth of the conclusion. For example, if under normal conditions water boils at 100°C, then when they change, for example, high in the mountains, it boils at a lower temperature.
• 4. Generalization without sufficient basis– in this case, generalization is made based on random characteristics or heterogeneous phenomena are generalized.

For example.

Charles XII invaded Russia by crossing the Berezina River

near the city of Borisov

Napoleon invaded Russia by crossing the Berezina River

near the city of Borisov

Hitler invaded Russia by crossing the Berezina River

near the city of Borisov

Apparently, this is the reason for the defeat of all these aggressors

The main disadvantage of popular induction is that the cause-and-effect relationship between phenomena remains unexplained. Scientific induction allows you to eliminate this drawback.