Induction, generalization, deduction

deductive

Deduction and presentation
It means to lay out 、 performance , Metaphor is the reasoning that inevitably draws a conclusion from the premise , Starting from some hypothetical propositions , Apply the rules of logic , The process of deriving another proposition , The conclusion under special circumstances is deduced from the general principle

inductive

1 Point around and make organized （ Mostly used for abstract things ）
2 Refers to a method of reasoning , Generalize the general principle from a series of specific facts （ Follow “ deductive ” relative ）
3 Induction in Mathematics , It refers to generalizing general concepts from many individual things 、 Thinking method of principle or conclusion .

Merger ; Close up . for example ： This is a conclusion drawn from a large number of facts

From part to whole , From special to general , From individual to general reasoning

Induction and deduction are the earliest human cognition 、 The most widely used way of thinking . It involves the relationship between individual and general , It is the external relationship between things and concepts . The so-called induction , It refers to generalizing general concepts from many individual things 、 Thinking method of principle or conclusion . Induction can be divided into complete induction and incomplete induction . Complete induction is the premise that all objects of this kind are included , So as to make a general conclusion about this kind of object . Incomplete induction is also called simple enumeration induction , Through observation and research , Discover a certain attribute inherent in something , And keep repeating without encountering the opposite case , Thus, it can be judged that all such objects have this attribute , Mathematical exhaustion is complete induction . The conclusion of simple enumeration induction has probability , May be true , It may also be false . In practice , People always deal with specific things , First, acquire the knowledge of these individual things , Then on the basis of these special knowledge , Generalize the universal knowledge of similar things . such as , From the macro world, everything can be divided into several levels , The fact that atoms in the microscopic world can be further divided into elementary particles and even quarks , obtain “ Matter is infinitely divisible ” The general principle of . This cognitive process includes inductive reasoning .

Generalization

Generalization is induction , blanket .

Generalization is a thinking process and method of forming concepts . That is, the essential attribute extracted from some things with some same attributes in thought , It is extended to all things with these attributes , Thus forming a general concept about such things .

A theoretical induction . By analyzing several things, we get their commonality , Therefore, all kinds of things have this characteristic .

Generalization （generalization）, A kind of thinking process . The human brain is based on comparison and abstraction , Integrate the common essential characteristics of abstracted things , And the process of extending it to similar things . For example, children often see birds , And compare it with other animals , Gradually distinguish the essential characteristics of birds （ There are feathers 、 Oogenesis, etc ） And non essential characteristics （ Can fly 、 size 、 Color, etc. ）; On this basis , These essential characteristics can be integrated , Animals with these essential characteristics are called birds . According to the level of generalization , It is divided into primary summary and advanced summary . The former refers to the generalization at the level of perception or representation , It is manifested in extracting common features or connections of things according to specific experience , Summarize the common attributes of certain things , It is the primary form of generalization , It is beneficial to the development of individual logical thinking , However, due to the limitations of specific experience, it is difficult to get the essential attributes of things , For example, children call flying animals birds . The latter refers to the generalization based on grasping the essential characteristics of things , It is a high-level form of generalization . All scientific concepts and theorems are the product of advanced generalization .

Generalization is related to abstraction . You can't generalize without abstraction . When abstracting and generalizing , Pay attention to discard the secondary 、 Non essential attribute , Put the main 、 Extract the essential attributes , Then by generalizing, it represents the whole of the same thing .

Generalization is an important method of scientific discovery . Because generalization is from a small range of understanding to a larger range of understanding ; It is the extension of knowledge from one field to another .

“ Generalization ” The English of the word is “generalization”,“ universality ” The word in English is “generality”. These two words have the same root in English , signify “ Generalization ” And “ universality ” There is a close connection .“ Generalization ” The word in 《 Modern Chinese dictionary 》 There are two meanings in , First, it means “ Sum up the common characteristics of things ”, First, it means “ concise ”. As a way of thinking , The summary is “ Separate from something in thought , A few objects have certain properties , All objects generalized to a certain kind of things have this attribute .” So generalization is a way of thinking to form a universal understanding .
Universal cognition may be about the surface characteristics of things , It may also be about the essential characteristics of things . such as “ Featherless , Bipedal animals ” This is a summary of human surface characteristics ：“ Be able to think abstractly with the help of language , Animals that can work ” Is a summary of the essential characteristics of human beings . A summary of the essential characteristics of things , It helps us form the concept and regularity of things , It has important cognitive value .
The generalization of the essential characteristics of things must rely on abstraction . Abstraction , Is analyzing 、 comprehensive 、 On the basis of comparison , The essential characteristics of things and things themselves , And other attributes of things , And put the essential characteristics to the primary position to understand . for example , We analyze people 、 Synthesis and comparison , In terms of color , There are white people 、 The black race 、 Yellow people and so on ; Judging from the height , There are big 、 Little one 、 Medium grade ; In terms of gender , There are men 、 Women wait . These are all about the individual attributes of people . And the essential attributes shared by all kinds of people , It is “ Be able to think with the help of language , Can work ”. Extracting this essential feature is called “ abstract ”, Extend this feature to all “ people ” Go to of , This is the generalization of human essential characteristics .

The difference between generalization and induction

Induction is a way of summarizing things , The result of induction is described in words , Generalization is the description of the result of induction .

The main difference between the two is ：

1. The order of thinking is different .

The essence of induction is the situation — result — The rules . The starting point of reasoning is to recognize the current situation , By recognizing the status quo , Get possible results , Then find out the common attributes from the results , From these common attributes, we can get the general rules 、 General rules .

The essence of deduction is rules — situation — result . Reasoning begins with rules or conclusions , Starting from the general rules , Analyze what may happen , From these situations , Get possible results .

2. The reasoning process is different .

Induction is a reasoning process from individual to general , Deduction is a reasoning process from general to individual , The two processes are exactly the opposite , The starting point and the result are just the opposite .

3. The relationship between premise and conclusion is different .

Induction is a summary of the current situation , It is a highly condensed version of some phenomena , Not all the current situations are proved , It does not include all the current situations and phenomena , Especially for incomplete induction , Although the premise is true , The reasoning process is also correct , But the conclusion may not be completely true , Because there may be black swan phenomenon , There may be some accidents .

Deduction is the deduction of general laws . There is an inevitable relationship between its premise and conclusion , The premise is true , The reasoning process is correct , The conclusion must be true .

4. The knowledge range of conclusion judgment is different .

Induction is the reasoning from individual things to general things , The knowledge range determined by the conclusion , It is completely beyond the scope of knowledge contained in the premise , It is the highly condensed of these phenomena or things 、 High summary .

Deduction is the reasoning from general things to individual things , The knowledge range determined by the conclusion , Not beyond the scope of knowledge in the premise , But the concrete embodiment of these general laws .

The connection between induction and deduction

Although induction and deduction are different , But the two are interrelated 、 Dialectical unity 、 Mutually causal .

Induction provides guidance for deduction , Pointed out the direction , Whether the conclusion of induction is correct , It needs to be proved by deduction to confirm . Deduction provides a theoretical basis for induction , It also provides a variety of possibilities for induction .

The conclusion of induction provides the premise and basis for deduction . Induction is a conclusion drawn from summarizing common things and phenomena in life , This conclusion may be axiom 、 Regulations 、 Rules, etc . The premise of deduction is these axioms we get through induction 、 Regulations 、 law . therefore , Deduction is based on induction , Induction prepares the conditions for deduction .

Reference resources ：
1.https://mp.weixin.qq.com/s/muztAlSBdvd6fBX3PItTTw
2.https://zhuanlan.zhihu.com/p/427254440