Inductive or inductive reasoning, sometimes called inductive logic, is the reasoning that derives general knowledge from individual knowledge and conclusions that may be true from known premises. According to the limited observation of special marks, it classifies features or relationships into types; Or a formula expresses a rule based on limited observation of repetitive phenomena patterns. For example, the following special proposition uses induction: ice is cold. Billiards move when they hit the club. Infer universal propositions such as: all ice is cold. There is no ice in the sun. For all operations, there are the same and opposite redo operations. People often add their own ideas to induction, which just helps people remember. One of the research methods of physics. The technique of inferring general information from sample information. To make a correct induction, we need to select a sample from the population, which must be large enough and representative. For example, when we buy grapes, we use induction. We usually taste them first. If they are all sweet, we conclude that grapes are all sweet, so we can buy a bunch with confidence. Inductive reasoning can also be called induction. Complete inductive reasoning is also called complete induction. Incomplete inductive reasoning is also called incomplete induction. Inductive method also includes logical methods to improve the confirmation degree of inductive premise to conclusions, namely, five methods of finding cause and effect, probability method, statistics method, and methods of collecting and sorting out empirical materials.
classify
Classical inductive method Classical inductive logic is an inductive theory founded by Bacon and developed by Mill. This paper mainly studies complete inductive reasoning, incomplete inductive reasoning (simple enumeration induction and scientific induction) and five methods of finding cause and effect. Aristotle discusses induction. He is talking about simple enumeration, induction and reasoning. For example, expert helmsman is the most effective. Therefore, people who know their major are the most effective. Luo Ji, the founder of classical induction, was Francis Bacon of England in the17th century. He first put forward the three-table method of sorting out and analyzing perceptual materials, that is, there are tables, missing tables and measuring tables. He believes that on this basis, special facts can be gradually added by excluding inductive methods such as induction. Finally, the most universal axiom is reached. John Mill was an English philosopher in the19th century and a master of classical inductive logic. By summarizing the research results of classical inductive logic since Bacon, he systematically discussed five methods of seeking cause: seeking common ground, seeking differences, seeking common ground and seeking differences, combining usage, * * variation and residual method, and made specific provisions and explanations on their forms and laws. Modern inductive method, also known as probabilistic logic, was founded by Magna Keynes and developed by Reichenbach and Carnap Cohen, and used probability theory, formal axiom method and other tools to explore the results of inductive problems. Classical inductive logic was questioned by Hume in Britain. He believes that the rationality of inductive reasoning cannot be guaranteed logically. The universal law of causality and the unity of nature on which inductive reasoning is based are just a habitual psychological association, and there is no objective truth. It is impossible to draw general conclusions from individual premises. Hume's questioning is thought-provoking. Since it is impossible to draw general conclusions from individual premises, can individual premises provide some evidence support for general conclusions, and what is the probability that premises support conclusions? This is the research topic of modern inductive logic, that is, probabilistic logic. The study of modern inductive logic began in the middle of19th century. Augustus de Morgan, Ye Fang-Si, Wen En and others all explored the study of induction by using classical probability theory. Keynes published in 192 1 that probability is a logical relationship between propositions, and on this basis, he constructed an axiomatic system of probability calculus. Modern inductive logic has been established. Reichenbach, published in 1934, advocated defining probability by the limit of relative frequency, and founded the theory of frequency probability, which made the study of modern inductive logic ...
Question 2: What is induction? Join at 40 points. Inductive argument is an argument method from individual to general. It draws a general conclusion through many individual examples or arguments, and then summarizes their characteristics. Induction can give examples before drawing a conclusion, or it can put forward a conclusion and prove it with examples. The former is what we usually call induction, and the latter is what we call example. Example method is an argument method to prove the argument with individual and typical concrete examples. Induction is an inference that leads to universal knowledge from individual knowledge and a conclusion that may be true from the premise of known truth. According to the limited observation of special marks, it classifies features or relationships into types; Or the formula expresses the law based on the limited observation of the repetitive phenomenon pattern.
Question 3: What is an inductive formula? The axiom of induction is the fifth axiom of five axioms about positive integers put forward by piano:
Let s be a subset of the set of positive integers, and
(1) 1 belongs to S.
(2) if n belongs to s, then n+ 1 also belongs to s.
So, s is a set of positive integers.
Mathematical induction, as a direct inference of inductive axiom, is widely used.
Also called reduction formula. In the proof theory, inductive axiom is an axiom of Piano's arithmetic system, which can be written as:
F(a)，―→a，F(aH)
F(o)，―→a，F(s)
Where aH is the successor of a, a does not appear in F(o) or a, and s is a note.
F(a) is called inductive formula. Mathematical induction is a special case of inductive axiom, which can be expressed as p (o) d (p (s) → p (s+ 1) → c ⅹ p (x). Often used to prove the nature of natural numbers. The inductive axiom means that if we can prove that the natural number O has the property of F and the derivative of any number A has the property of F, then any term has the property of F..
Question 4: What is induction? The basic definition of induction (guī nà): ① Get together and make it orderly (mostly used in abstract things): The opinions put forward by everyone are mainly these three points. (2) A method of reasoning, which generalizes Ding's general principle (as opposed to deduction) from a series of concrete facts. In addition, the so-called induction in mathematics refers to the thinking method of summarizing general concepts, principles or conclusions from many individual things.
Usually only understand the meaning of the above paragraph.
In addition to this basic meaning, induction is a mathematical term.
Like mathematical discovery, mathematical problem solving is usually based on exploratory methods such as analogy and induction, and then the conclusion or conjecture of the solution is obtained, and then the conjecture is proved or denied, so as to achieve the purpose of solving the problem. Analogy and induction are two important ways to get a guess. The so-called induction method refers to a form of reasoning that draws general conclusions through the analysis of special cases. It consists of two parts: the premise is a number of known individual facts, which are individual or special judgments and statements, and the conclusion is a guess drawn from the premise, which is a general statement and judgment. Its thinking mode is: Let MI (I = 1, 2, ..., n) be the research object.
In addition to mathematical terms, induction is a logical term.
Logical noun
concept
Induction and deduction are the earliest and most widely used thinking methods. It involves the relationship between the individual and the general, and the external relationship between things and concepts. The so-called induction refers to the way of thinking that summarizes general concepts, principles or conclusions from many individual things. Induction can be divided into complete induction and incomplete induction. Complete induction is a method to make a general conclusion about this kind of object on the premise of including all of it. Incomplete induction, also known as simple enumeration induction, is a reasoning method that finds a certain attribute inherent in a certain kind of things through observation and research, and repeats it repeatedly without encountering negative examples, so as to judge that such objects all have this attribute. Mathematical exhaustive method is a complete decomposition method. The conclusion of simple enumeration induction is probable, which may be true or false. In practice, people always get the knowledge of these individual things when dealing with specific things, and then sum up the general knowledge of similar things on the basis of these special knowledge. For example, everything in the macro world can be divided into several levels, and atoms in the micro world can be subdivided into elementary particles and quarks, and people come to the general principle that "matter is infinitely separable". This cognitive process includes inductive reasoning.
Dialectical relationship between induction and deduction
Induction and deduction reflect people's way of thinking in two opposite directions of understanding things. The former is the thinking movement from individual to general, and the latter is the thinking movement from general to individual. Induction and deduction are the thinking methods of formal logic and dialectical logic, and they are the starting point of dialectical thinking. The difference is that formal logic regards induction and deduction as independent and parallel proof tools and reasoning rules, which separates the dialectical relationship between induction and deduction. Moreover, formal logic puts aside the specific content and contradiction of things and only pays attention to the form of induction and deduction, so it always starts from the unchangeable premise and draws rigid conclusions according to fixed lines. Contrary to formal logic, dialectical logic emphasizes that induction and deduction are two different and interrelated ways of thinking, which are inseparable aspects of the formation of concepts and theories.
Question 5: What do you mean by sorting and induction? The so-called induction is concentration, the so-called summary is conclusion, and inductive summary is the conclusion of concentrating something. For example, the theme of an article comes from induction and summary.
Question 6: What is induction? The so-called inductive reasoning refers to the reasoning that all objects of a class have certain properties according to the fact that some objects have certain properties, which is called inductive reasoning (induction for short). Induction is a process from special to general, which belongs to reasonable reasoning.
Question 7: What is a summary? Summary:
Analyze and study the relevant situation at a certain stage and make instructive conclusions; Summarize the situation and make it orderly.
Question 8: What is the systematic summary of inductive theory and practice and the scientific sublimation of theory?
Land is the material basis for human survival and development, the most basic means of labor for social production and the source of all production and existence. No matter how advanced modern technology is, without land, we will have nothing. William? Patty has a saying: "Land is the mother of wealth, and labor is the father of wealth." Rural land is the most primitive means of production for agricultural development, which provides a solid foundation for rural development and is the basic means of production and living for farmers' survival and development. In the new era, land, as a factor of production, can only be fully "flowing" and become a tree with living water and roots, so as to further realize the scientific allocation with labor, capital, technology and other factors and truly play its role as "the foundation of agricultural production, the source of farmers' wealth and the root of rural development".
Reform conforms to the trend and innovation responds to change. At present, the rural land system reform is experiencing new ice-breaking and new innovation. 20 1 14 10, the Central Committee of the Communist Party of China and the State Council issued the Opinions on Guiding the Orderly Circulation of Rural Land Management Right and Developing Moderate Scale Operation of Agriculture, and in February of 20 15, they also issued the Opinions on Rural Land Expropriation, Collective Management Construction Land Entering the Market and Homestead System Reform, revealing the rural areas.
Inductive or inductive reasoning, sometimes called inductive logic, is the reasoning that derives general knowledge from individual knowledge and conclusions that may be true from known premises. According to the limited observation of special marks, it classifies features or relationships into types; Or a formula expresses a rule based on limited observation of repetitive phenomena patterns. One of the research methods of physics. The technique of inferring general information from sample information. To make a correct induction, we need to select a sample from the population, which must be large enough and representative. For example, when we buy grapes, we use induction. We usually taste them first. If they are all sweet, we conclude that grapes are all sweet, so we can buy a bunch with confidence. Inductive reasoning can also be called induction. Complete inductive reasoning, also called complete induction. Incomplete inductive reasoning is also called incomplete induction. Inductive method also includes logical methods to improve the confirmation degree of inductive premise to the conclusion, namely, five-check causality method, probability method, statistics method and the method of collecting and sorting out empirical materials.
Question 9: What are inductive summary method and inductive memory method? Inductive summary method is a method of summarizing the learned content according to certain standards, and then summarizing the attributes and laws through comparative analysis. Inductive memory method is a kind of memory method that summarizes the contents of memory according to different attributes, and then remembers these contents and their attributes in different categories.