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Lecture notes, cheat sheets
Logics. Induction. Concept, rules and types (lecture notes)
Directory / Lecture notes, cheat sheets Table of contents (expand) LECTURE No. 17. Induction. Concept, rules and types 1. The concept of induction Concepts such as general and particular can only be considered in conjunction. None of them has independence, since when considering the processes, phenomena and objects of the surrounding world only through the prism of, say, a private picture, the picture will turn out to be incomplete, without many necessary elements. A too general look at the same objects and the picture will also give too general, the objects will be considered too superficially. In order to illustrate what has been said, a humorous story about a doctor can be given. One day the doctor had to treat a tailor who had a fever. He was very weak and the doctor thought that his chances of recovery were slim. However, the patient asked for ham and the doctor allowed it. After some time, the tailor recovered. In his diary, the doctor made a note that "ham is an effective remedy for fever." After a while, the same doctor treated the shoemaker, who also had a fever, and prescribed ham as a medicine. The patient died. The doctor wrote in his diary that "ham is a good remedy for fever in tailors, but not in shoemakers." Induction is the transition from the particular to the general. That is, this is a gradual generalization of a more particular, specific concept. In contrast to deduction, in which a true conclusion, reliable information, is derived from true premises, in inductive reasoning, even from true premises, a probabilistic conclusion is obtained. This is due to the fact that the truth of the particular does not uniquely determine the truth of the general. Since the inductive conclusion is probabilistic in nature, further construction of new conclusions on its basis can distort the reliable information received earlier. Despite this, induction is very important in the process of cognition, and one does not have to look far to confirm this. Any position of science, whether it be humanitarian or natural science, fundamental or applied, is the result of generalization. At the same time, generalized data can be obtained in only one way - by studying, considering the objects of reality, their nature and relationships. Such a study is a source of generalized information about the patterns of the world around us, nature and society. 2. Rules of induction In order to avoid mistakes, inaccuracies and inaccuracies in one's thinking, to avoid curiosities, one must comply with the requirements that determine the correctness and objective validity of an inductive conclusion. These requirements are discussed in more detail below. The first rule states that inductive generalization provides reliable information only if it is carried out according to essential features, although in some cases one can speak of a certain generalization of non-essential features. The main reason that they cannot be generalized is that they do not have such an important property as repeatability. This is all the more important because inductive research consists in establishing the essential, necessary, stable features of the phenomena being studied. According to second rule An important task is to accurately determine whether the phenomena under study belong to a single class, recognizing their homogeneity or same type, since inductive generalization applies only to objectively similar objects [8]. The validity of the generalization of features that are expressed in particular premises can depend on this. Incorrect generalization can lead not only to misunderstanding or distortion of information, but also to the emergence of various kinds of prejudices and misconceptions. The main reason for the occurrence of errors is generalization by random features of single objects or generalization by common features, when there is no need for these features. The correct application of induction is one of the pillars of correct thinking in general. As stated above, inductive reasoning - this is an inference in which thought develops from knowledge of a lesser degree of generality to knowledge of a greater degree of generality [9]. That is, a particular subject is considered and generalized. Generalization is possible to certain limits. Any phenomenon of the surrounding world, any subject of research is best studied in comparison with another similar subject. So is induction. Its features are best demonstrated in comparison with deduction. These features manifest themselves mainly in the way the inference process takes place, as well as in the nature of the conclusion. Thus, in deduction one concludes from the characteristics of a genus to the characteristics of a species and individual objects of this genus (based on volumetric relations between terms); in inductive inference - from the characteristics of individual objects to the characteristics of the entire kind or class of objects (to the volume of this characteristic) [10]. Therefore, there are a number of differences between deductive and inductive reasoning that allow us to separate them from each other. Can be identified several features of inductive reasoning: 1) inductive reasoning includes many premises; 2) all premises of inductive reasoning are single or private judgments; 3) inductive reasoning is possible for all negative premises. 3. Types of inductive reasoning First, let's talk about the fundamental division of inductive reasoning. They are complete and incomplete. Complete are called inferences, in which the conclusion is made on the basis of a comprehensive study of the entire set of objects of a certain class. Complete induction is used only in cases where it is possible to determine the entire range of objects included in the class under consideration, that is, when their number is limited. Thus, complete induction applies only to closed classes. In this sense, the use of complete induction is not very common. Moreover, such an inference gives a reliable value, since all the objects about which the conclusion is made are listed in the premises. The conclusion is made only concerning these subjects. In order to be able to talk about complete induction, it is necessary to verify compliance with its rules and conditions. Thus, the first rule says that the number of objects included in the class under consideration must be limited and determined; their number should not be large. Each element of the class taken, with respect to which an inference is created, must have a characteristic feature. And finally, the derivation of a complete conclusion must be justified, necessary, rational. The scheme of a complete inference can be reflected as: 51 - P 52 - P 53 - P Sn - R. An example of a complete inductive inference. All guilty verdicts are issued in a special procedural order. All acquittals are issued in a special procedural order. Guilty verdicts and acquittals are decisions of the court. All court decisions are issued in a special procedural order. This example reflects the class of objects - court decisions. All (both) of its elements were specified. The right side of each of the premises is valid in relation to the left. Therefore, the general conclusion, which is directly related to each case separately, is objective and true. Despite all the undeniable advantages and advantages of full induction, there are often situations in which its use is difficult. This is due to the fact that in most cases a person is faced with classes of objects, the elements of which are either unlimited or very numerous. In some cases, the elements of the class taken are generally inaccessible for study (due to remoteness, large dimensions, poor technical equipment or low level of available technology). Therefore, incomplete induction is often used. Despite a number of shortcomings, the scope of incomplete induction, the frequency of its use is much greater than the full one. Incomplete induction called an inference, which, on the basis of the presence of certain recurring features, ranks this or that object in the class of objects homogeneous to it, which also have such a feature. Incomplete induction is often used in human everyday life and scientific activity, as it allows one to draw a conclusion based on the analysis of a certain part of a given class of objects, saving time and effort. At the same time, we must not forget that as a result of incomplete induction, a probabilistic conclusion is obtained, which, depending on the type of incomplete induction, will fluctuate from less probable to more probable [11]. The scheme of incomplete induction can be represented as: 51 - P 52 - P 53 - P S1, S2, S3... constitute class K. Probably each element K - R. The above can be illustrated by the following example. The word "milk" changes by case. The word "library" changes by case. The word "doctor" changes by case. The word "ink" changes by case. The words "milk", "library", "doctor", "ink" are nouns. Probably all nouns change by case. Depending on how the conclusion of the conclusion is justified, it is customary to divide incomplete induction into two types - popular and scientific. Popular incomplete induction, or induction by simple enumeration, does not consider the objects and classes to which these objects belong in very depth. Thus, based on the repetition of the same characteristic in a certain part of homogeneous objects and in the absence of a contradictory case, a general conclusion is made that all objects of this kind possess this characteristic. As the name suggests, popular induction is very common, especially in non-scientific environments. The probability of such an induction is low. When forming a popular inductive reasoning, one should be aware of possible errors and prevent their occurrence. A hasty generalization means that the conclusion takes into account only that part of the facts that speaks in favor of the conclusion made. The rest are not considered at all. For example: Winter in Tyumen is cold. It is cold in Urengoy in winter. Tyumen and Urengoy cities. All cities are cold in winter. After, therefore, for a reason - means that any event, phenomenon, fact preceding the one under consideration is taken as its cause. The substitution of the conditional for the unconditional means that the relativity of any truth is not taken into account. That is, the facts in this case can be taken out of context, changed places, etc. At the same time, the truth of the results obtained continues to be affirmed. Scientific induction, or induction through the analysis of facts, is an inference, the premises of which, along with the repeatability of a characteristic in some phenomena of the class, also contain information about the dependence of this characteristic on certain properties of the phenomenon. That is, unlike popular induction, scientific induction is not limited to a simple statement. The subject under consideration is subjected to deep research. In scientific induction, it is very important to comply with a number of requirements: 1) research subjects should be selected systematically and rationally; 2) it is necessary to know as deeply as possible the nature of the objects under consideration; 3) understand the characteristic features of objects and their relationships; 4) compare the results with previously fixed scientific information. An important feature of scientific induction, which determines its role in science, is the ability to reveal not only generalized knowledge, but also causal relationships. It was through scientific induction that many scientific laws were discovered. Author: Shadrin D.A. << Back: Syllogism (The concept of syllogism. Simple categorical syllogism. Complex syllogism. Abbreviated syllogism. Abbreviated complex syllogism) >> Forward: Methods for establishing cause-and-effect relationships (The concept of cause-and-effect relationships. Methods for establishing cause-and-effect relationships)
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