The method of similarity as a method of scientific induction. The method of similarity as a method of scientific induction Under conditions A1, B, C, the phenomenon “a1” arises
This method is as follows. Let's say we are looking for the cause of some phenomenon a. From observation we know that the phenomenon of a mass occurs under ABC circumstances. Circumstance ABC is complex, it is a combination of different parts (elements): A, B, C. Which part (element) of this complex circumstance (A or B, or C) is the cause of phenomenon a based on observation of only one case of connection between a and circumstance ABC cannot be said. Then we set ourselves the task of finding several cases when phenomenon a exists. By observing, we establish that the phenomenon of mass also occurs under circumstances AD and under circumstances AFD *
Comparing these three cases, we find that phenomenon a occurs under circumstances (ABC, ADE, AFG) that are different in everything and similar in only one way - they all have the same circumstance A, since circumstances B, C, D , E, F, G cannot be the cause of a, since phenomenon a occurs even in the absence of any of these circumstances, it is concluded that the cause of phenomenon a is the only circumstance A that is similar in all cases.
The conclusion using the single similarity method can be written in the following diagram:
Example. In one district 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 communication office to the second by Sasha's cab driver. In all three cases, different persons sent and received mail: on August 4 - Petrenko and Ivanenko, on December 20 - Nikolaenko and Yakovenko, on December 25 - Vorona and Savchenko. On this basis, the investigator put forward a version that the theft was committed by cab driver Sashin.
In the form of a diagram, this conclusion can be written as follows:
The application of the single similarity method consists of three successive stages.
1. First of all, we establish all those cases where there is a phenomenon and the cause of which we find out.
2. Then each case is analyzed and the circumstances under which phenomenon a occurs are identified.
3. After this, circumstances common to all these cases are found, which are the cause of the phenomenon and what interests us.
The conclusion using the single similarity method is based on the following rule: if two or more cases of the phenomenon being studied have only one circumstance in common, and all other circumstances are different, then this only similar circumstance is the cause of this phenomenon.
The single similarity method produces conclusions that are not reliable, but probable. The degree of probability of a conclusion depends on various conditions: a) on the number of cases considered. The more cases examined, the more likely the conclusion will be; b) from the depth and thoroughness of the study of all the circumstances, from the accuracy of establishing that in all cases only one was similar; c) the degree of probability of a conclusion using the method of single similarity depends only on how significant the differences are in all circumstances, except for the only similar thing that we define as the cause. The more differences in circumstances, the more likely the conclusion will be that the cause of the phenomenon that interests us is the circumstance that turned out to be the same in all cases.
In conclusions using the method of single similarity, one should also keep in mind taxes. In some cases, it may be that the only similar circumstance taken as the cause is itself complex and the cause of the phenomenon under study is not the entire circumstance, but only some part of it, which must be determined. In other cases, it may turn out that the circumstance taken as the cause does not act on its own, but together with others, that is, only part of the cause or one of the causes, and we incorrectly considered it the only cause.
The single similarity method is often used in investigative practice to put forward versions of a case.
Logics. Exam
Option #1.
Give an example of reasoning using the residual method.
Residual method occurs when a certain network of causes causes in turn a network of phenomena. In this case, the connections of determination are differentiated according to direct cause-and-effect relationships.
K ¾ M
Probably L - Q
For example, there was a robbery. The investigator looks at who was involved in such cases. Three people were identified: Ivanov, Petrov. Sidorov. Subsequently, it turned out that Petrov was visiting, Ivanov was at work, but Sidorov’s whereabouts could not be established. Therefore, Sidorov could have committed the robbery.
2. Reverse judgment: not all yogurts are created equal.
J: Some yoghurts are healthy.
1) transformation: SJP – SOP(-)
A: Some yoghurts are not healthy to eat.
2) address: SJP – PJS
J: Some equally healthy eating yogurts.
3. Restore and check the enthymeme: not every TV shows well, since many TVs are of poor quality.
B.p. E: Many TVs are not of high quality
M.p. J: Some TVs have good display
A: Some items that show well are not of high quality.
The conclusion follows from figure III.
In the third figure of a simple categorical syllogism, the middle term is in the place of the subject in both premises. The third figure has the following rules:
1. The minor premise is always an affirmative proposition.
2. Conclusion is always a private judgment.
M.p. M-S
4. Make a diagram and check the correctness: the river is moving or not moving, scientific research has shown that the river is moving, therefore, the river cannot help but move.
The river is moving - and
((a ˅not a)^a)->a
Let's prove the proposition by contradiction.
Justify the mode JAJ IV of the figure.
IV figure
In the fourth figure of a simple categorical syllogism, the middle term in the major premise is in the place of the predicate, and in the minor, in the place of the subject. As you can see, according to the structure the fourth figure is a mirror image of the first. It is ponderous, and thinking most often spontaneously leads it to the first figure.
6. Is the following definition correct (if not, why, indicate errors): a document is a business paper confirming a fact or right to something.
This is a real, explicit definition. The definition is given incorrectly, since the rule of observance of volume is violated; the volumes are not identical.
Theory, explanation: A real definition is one through which the essential characteristics of what is conceivable in the concept of an object or class of objects are revealed.
Rules for defining concepts:
1. Volumes Dfd and Dfn must be identical. If the volumes are not equal, we will have either a definition that is too narrow or too broad. The first occurs when, instead of species-forming characteristics, the characteristics of a subspecies or individual characteristics are indicated. For example, “logic is the science of concepts.” The second occurs when Dfd is not subsumed under the closest genus, or when, instead of a species-forming characteristic, a characteristic common to several species-specific concepts is indicated. For example, “The Moon is a satellite of the Earth.” The definition is broad, since in addition to the Moon there are also artificial satellites of the Earth.
Option number 2.
Give an example using the similarity method.
Similarity method.
(Q)MLA-d
Probably A(Q) - d
The similarity method occurs when, in a network of heterogeneous phenomena that precede a certain event, we encounter a repeating phenomenon and assume it as a possible cause.
Example: The Roman scientist Philodemus, who recorded the plague at the beginning of our century, noticed that both poor and rich people got sick; both those who live in the mountains and those who live in the lowlands. However, they all drink water from the same source. Conclusion: Water is likely the cause of their illness. The probability of the conclusion is due to the fact that a possible cause Q is assumed, which is not fixed by empirical research, but which may be the real cause of the event under study.
2.Transform judgment: Some people rarely think about the meaning of their lives.
J: Some people rarely think about the meaning of their lives.
Transformation: SJP – SOP(-)
O: Some people do not rarely think about the meaning of their lives.
Theory: Transformation is a type of transformation when, based on the relationship of the subject to the predicate, the relationship of the subject to the concept that contradicts the predicate is established. The inverted form is essentially a double negation, when we assert: if it is not true that A is not, then, therefore, A is true.
3. Restore the enthymeme: snow is always white. Not a single winter is complete without snow.
Snow is always white
Winter is the white season
No winter is complete without snow
The reasoning goes according to figure 2.
In the second figure of a simple categorical syllogism, the middle term is in the place of the predicate in both premises. The second figure also has its own special rules. 1. The major premise is always a general judgment. 2. One of the premises is always a negative judgment.
M.pS -M
4. Check the reasoning: if a black cat crossed your path, then you need to spit over your right shoulder, and if you spit over your right shoulder, then you can hit a passerby, if you hit a passerby, then he will hit you in the eye, if he hits you in the eye, then a black eye will appear under your eye, which means that if a black cat crosses your path, then there will be a black eye under your eye.
(a->b)^(b->c)^(c->d)^(d->e)->(a->e).
The law of hypothetical syllogism, or purely conditional inference.
As we see, in a purely conditional inference both the premises and the conclusion are conditional propositions, and the ontological basis of the conclusion is cause-and-effect dependencies. Thus, we see that the consequence B in the first premise is the basis for the consequence C in the second premise.
In general, this law allows us, if in the process of reasoning we come across a chain of cause-and-effect dependencies, to omit intermediate connections and use the initial cause and final effect.
Related information.
The single similarity method is based on such properties of causality as precedence, necessity And universality. This method consists of an attempt to identify, among the conditions of the phenomenon of interest to us, a phenomenon that constantly precedes this phenomenon. The latter phenomenon in this case is considered the probable cause of this phenomenon.
Let us look for the cause of the phenomenon X among the conditions a, b, c, d, e. Then single similarity method can be formulated as follows:
If some condition F constantly precedes the occurrence of the phenomenon X under study while other conditions change, then this condition is probably the cause of the phenomenon X.
We present a diagram of this method for five conditions.
Subject to conditions a, b, c, d, but in the absence e occurs X.
Subject to conditions a, b, c, e, but in the absence d occurs X.
Subject to conditions a, c, d, e, but in the absence b occurs X.
Subject to conditions b, c, d, e, but in the absence A has a mesro X.
Hence, With there probably is reason x.
Example. Hot water was poured into a glass and the glass burst.
A glass of cold water was placed in a hot oven, the glass burst.
A lamp was placed near the mirror, and a crack formed on the glass.
Therefore, the cause of glass failure is probably
sudden heating.
Let's denote: a- glass shape, b- sudden heating, With- water, d- bake, e- mirror shape, f- lamp, X- glass destruction.
Then you get the following diagram:
In the presence of a, b, c occurs X.
In the presence of a, b, d occurs X.
In the presence of e, f, b occurs X.
Hence, b is probably cause x.
The structure of a real inference does not completely coincide with the diagram, but the existing coincidence is quite enough to recognize the method of single similarity.
Methods for establishing a causal relationship are used not only in experimental sciences such as physics, chemistry, etc., but also in the humanities, medical diagnostics and investigative practice.
Example. In the sports and entertainment badminton club "Yantarny Shuttlecock" during training there were three cases of theft of unique shuttlecocks made from Siberian ostrich feathers: December 6, December 8, December 10, 2000. The investigator determined the circle of persons who had access to the coaching room and compiled the following table:
From this, the investigator concluded that Kinshin was most likely the culprit of the theft, since it was he and only he who entered the trainer’s room every time the theft occurred, and all the other faces changed.
Warning. The similarity method, although it allows us to put forward hypotheses and versions with a high degree of confidence, nevertheless has significant disadvantages, similar, firstly, to errors of induction through simple enumeration, since here attention is also drawn primarily to the similarity of the studied conditions for the appearance of a certain phenomenon , and, secondly, with the errors encountered in divisive conclusions. The rows of our table indicate that the theft was committed either by Kuldyshev, or Kinshin, or Sandler, or Kuznetsov, or Chuikin, or Shiroglazov. But we know that in all disjunctive inferences the “incomplete list of alternatives” error is possible. So in this case, it is possible that during all these days the cleaning lady Khapugina was working, who during the cleaning kicked out all the workers from the training room, where the precious shuttlecocks were located, and she remained there for some time. In this case, the fact that Kinshin had access to the training room on all the days when the theft took place will turn out to be a mere coincidence.
“...if two or more cases of a phenomenon to be studied have only one circumstance in common, then this circumstance - in which alone all these cases agree - is the cause (or consequence) of this phenomenon.”
John Stuart Mill, A System of Syllogistic and Inductive Logic. Statement of the principles of evidence in connection with methods of scientific research, M., 1914, Ed. G. A. Leman, p. 354.
EXAMPLE. “Let A = a pendulum of length 1, in a state of oscillation; B = pendulum made of iron; C = pendulum made of copper; a = oscillations of a pendulum have amplitude a. With this in mind, complex AB reads as “an iron pendulum of length 1 is in a state of oscillation,” complex AC is read as “a copper pendulum of length 1 is in a state of oscillation.” Here, a similar circumstance is the same length of the pendulum.
Let → denote causality. Then, according to the similarity method, the following conclusion is valid:
The conclusion reads as follows: if observation establishes that an iron and copper pendulum of (equal) length 1 in a state of oscillation both have an amplitude a, which means equal length 1 (a Not the material from which the pendulums are made) is the reason for the same amplitude a.
Therefore, induction is valid: the length of the pendulum is the cause of a certain amplitude of its oscillation.”
Svetlov V.A., History of the scientific method, M., “Academic Project”; "Business book", 2008, pp. 197-198.
Examples of using the similarity method to solve scientific problems
EXAMPLE. In 1906, chemists discussed two conflicting hypotheses:
Each plant, taking into account the different conditions of their growth, has its own type of chlorophyll;
Each plant has one type of chlorophyll.
Over the course of two years, the German chemist Richard Martin Willstetter, together with his assistants, analyzed more than 200 plants: terrestrial and aquatic, from valleys and mountain slopes, from the north and south, from rivers, lakes and seas... And from each specimen obtained, chlorophyll and its chemical composition was carefully analyzed. As a result, scientists were convinced that the composition of chlorophyll is the same everywhere (more precisely, there are two almost identical forms of it a And b).
The scientists gave this assessment of the conflicting hypotheses put forward earlier by other researchers: these studies were carried out “... with crude chlorophyll. As a matter of fact, it wasn’t chlorophyll at all.”
1. Similarity method
Using the similarity method, several cases are compared, in each of which the phenomenon under study occurs; Moreover, all cases are similar in one case and different in all other circumstances.
The method of similarity is called the method of finding commonality in differences, since all cases are noticeably different from each other, except for one circumstance.
The logical mechanism of inductive inference using the method of similarity presupposes a number of cognitive prerequisites.
(1) General knowledge about the possible causes of the phenomenon under study is required.
(2) From the preceding ones, all circumstances that are not necessary for the action under study and thereby do not satisfy the basic property of a causal relationship must be excluded (limited).
(3) Among the many preceding circumstances, those that are similar and repeated in each of the cases considered are identified, 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 examined 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.
A reliable conclusion can be obtained using the similarity method only if the researcher knows exactly all the preceding 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 takes on demonstrative significance.
2. Distinction 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, because the compared cases coincide with each other in many properties.
The method of difference is used both in the process of observing phenomena in natural conditions and in 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) It requires general knowledge of antecedent circumstances, each of which may be the cause of the phenomenon under investigation.
(2) From the terms of the disjunction, circumstances that do not satisfy the sufficiency condition for the action under study should be excluded.
(3) Among the many possible causes, there remains only one circumstance that is considered as the actual cause.
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 based on 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.
3. United method of similarities and differences
This method is a combination of the first two methods, when, by analyzing many cases, both the similar in the different and the different in the similar are discovered.
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.