What are the specific examples of inductive reasoning

Specific examples of inductive reasoning:

1. Mendeleev.

Using inductive reasoning and other methods, the properties of 63 elements and the relationship between atomists were studied, and the periodic law of chemical elements was summarized.

Causal links between chemical elements are revealed.

2. Right triangle.

The sum of the inner angles is 180 degrees. Acute triangle.

The sum of the inner angles is 180 degrees. Obtuse triangles.

The internal intersection is 180 degrees. Right triangles, acute triangles, and obtuse triangles are all triangles. So, the sum of the internal angles of all triangles is 180 degrees.

Inductive reasoning is a type of reasoning that goes from the individual to the general. Transition from a certain degree of perspective on individual matters to a broader point of view, and derive general principles and principles from special and specific examples. The general in nature and in society exists in the individual, in the particular, and through the individual.

The general exists in concrete objects and phenomena, so the general can only be known by knowing the individual. When people explain a larger thing, they summarize and generalize all kinds of general principles or principles from individual and special things, and then it is possible to start from these principles and principles and then draw conclusions about individual things.

This order of knowledge runs through people's interpretive activities, constantly rising from the individual to the general, that is, from the understanding of individual things to the understanding of the general regularity of things. For example, in view of the backwardness of social life caused by the lack of development of productive forces in various regions and in various historical periods, it can be concluded that the development of productive forces is the driving force of social progress.

This is precisely the process of reasoning that leads to general conclusions from the study of individual things, i.e., inductive reasoning. Obviously, inductive reasoning is the process of inference from understanding and studying individual things to summarizing and generalizing general laws.

In generalizing and generalizing, the interpreter uses not only inductive reasoning, but also deductively.

In people's interpretive thinking, induction and deduction are interrelated, complementary and inseparable.

Inductive reasoning is a method of reasoning that observes and collects specific cases or facts, from which general conclusions or laws are deduced. Here are a few specific examples of inductive reasoning:

1.Multiple apples have been observed falling to the ground after falling from the tree, and it can be inferred that all apples fall to the ground when they fall from the tree. This is a general conclusion drawn from the observation of multiple specific cases.

2.Suppose a student is late multiple times during a semester and none of the other students are late, it can be inferred that the student has a tendency to be late. This is a general conclusion based on observations in a number of specific cases.

3.After multiple people are observed to get sick after eating expired food, it can be inferred that expired food may cause health problems. This is a general conclusion based on observations in a number of specific cases.

4.By comparing the development experiences of several different countries, it can be inferred that there is a positive correlation between education level and economic development. This is a general conclusion drawn by looking at the situation in different countries.

5.Assuming that all employees of a company wear a work ID card provided by the company while working, it can be inferred that the company has a requirement for employees to wear work cards. This is a general conclusion drawn from the observation of multiple specific cases.

These examples illustrate the process of inductive reasoning, from which general conclusions or patterns are deduced by observing and gathering common features or patterns in specific cases. However, it is important to note that there may be biases or exceptions to the conclusions reached by inductive reasoning, so different factors need to be carefully evaluated and considered when conducting inductive reasoning.

Inductive reasoning is a type of reasoning that draws general conclusions from a series of specific facts or observations. Here are some specific examples of inductive reasoning:

1.Observation of natural phenomena: For example, drawing general conclusions about weather systems from the observation of a range of weather phenomena (e.g., rain, snow, storms).

2.Medical diagnosis: The doctor observes the patient's symptoms, signs, and examination results to summarize the patient's general disease, so as to determine the best method and the best plan.

3.Social science research: By observing and analyzing a range of individual behaviors and interactions, researchers can generalize social patterns and patterns of human behavior.

4.Business Analysis: Through the study of market trends, competitors, and consumer behavior, companies derive general conclusions about the business environment to guide strategic and business decisions.

5.Archaeology: By excavating and analyzing ancient human relics and relics, archaeologists can draw general conclusions about ancient human societies, cultures, and history.

6.Psychology: Through the study of an individual's behavior, emotions, and thought patterns, psychologists can draw general conclusions about the human psyche that can provide guidance for the intervention process.

7.Economics: Through the study of market behavior, supply and demand, and money flows, economists can draw general conclusions about the economic system to guide policymaking and economic development.

These examples show that inductive reasoning has a wide range of applications in a variety of fields and can help us better understand and respond to complex phenomena and problems.

Inductive reasoning is a way of reasoning from the particular to the general, by observing and analyzing specific examples, generalizing general laws or conclusions. Here are some specific examples of inductive reasoning:

1.It is observed that every apple is red, so it is inferred that all apples are red.

2.Find a cat and find that it has characteristics such as hair, four legs, etc., so it is inferred that other cats will also have these characteristics.

3.By looking at the sales data in the market, it is found that in the past few months, the sales of umbrellas have increased significantly after each rain, so it is inferred that the sales of umbrellas will also increase after the next rain.

4.In a mathematical problem, a pattern of a series of numbers is observed, such as 1, 3, 6, 10, 15, etc., and by analyzing the pattern of patterns, it can be deduced that the next number is 21.

5.By looking at multiple samples, it was found that all the daytime would have sun, so it was inferred that there would be sun during the day.

These examples are all processes of observing and deducing general laws or conclusions. However, inductive reasoning does not always have absolute accuracy, so it is necessary to combine other evidence and experience to verify or revise the inferences.

Examples of the development of scientific inductive reasoning:

1. Mendeleev used inductive methods and other methods to study the properties of 63 elements and the relationship between atoms, including the periodic law of chemical elements and revealing the causal relationship between chemical elements.

2. For example, Boyle's law on gas pressure, volume and temperature.

3. Faraday's law on electromagnetic interaction.

4. On the law of survival competition in biological evolution.

5. The volume of gold expands after heating; Silver expands in volume when heated; Copper expands in volume when heated; Iron expands in volume when heated.

Because after the metal is heated, the cohesion of the molecules is weakened, the molecular movement is accelerated, and the distance between the molecules increases, which leads to expansion, and gold, silver, copper, and iron are all metals; So, all metals expand in volume when heated.

The form of scientific inductive reasoning is as follows:

s1 is p; S2 is p......SN is p.

s1，s2，…, sn is a partial object of the s class, where no si(1 i n) is not p; And scientific studies have shown that there is a causal link between S and P.

So, all s are p.

The role of scientific inductive reasoning

Scientific inductive reasoning is also widely used in everyday life and scientific research.

Its role is as follows: to open up areas of knowledge and expand new knowledge; Assist the argument and enhance the persuasiveness of the argument.

In order to improve the reliability of scientific inductive reasoning conclusions, the following two points must be noted: the object under investigation must be typical; It must be guided by a scientific theory that can theoretically explain the causal connection between the object and its properties.

The above content refers to: Encyclopedia - Inductive Reasoning.

Encyclopedia – Scientific Induction.

Encyclopedia – Scientific Inductive Reasoning.

In fact, many concepts in science are based on incomplete inductions.

For example, "swans are white" is only an inference based on the fact that many swans are white, and does not fully summarize all swans.

For example: in a plane,Right triangleThe sum of the inner angles is 180 degrees. Acute triangle. The sum of the inner angles is 180 degrees. Obtuse triangles. The sum of the inner angles is 180 degrees. Right triangles, acute triangles, and obtuse triangles are all triangles.

Therefore, the sum of the internal angles of all triangles in the plane is 180 degrees.

This example is an individual knowledge of the inner angles of right-angled, acute, and obtuse triangles, and are all 180 degrees.

The general conclusion that "the sum of the internal angles of all triangles is 180 degrees" is inductive reasoning.

Classification

Traditionally, inductive reasoning has been divided into complete inductive reasoning and incomplete inductive reasoning, depending on the scope of the object examined by the premise. Completely inductive reasoning examines all the objects of a certain class of things, while incomplete inductive reasoning examines only a part of the objects of a certain class of things. Furthermore, according to whether the premise reveals the causal relationship between the object and its attributes, the incomplete inductive reasoning is divided into simple enumerative inductive reasoning and scientific inductive reasoning.

Modern inductive logic is the study of probabilistic reasoning and statistical reasoning. The premise of inductive reasoning is a necessary condition for its conclusion.

Second, the premise of inductive reasoning is true, but the conclusion is not necessarily true, but may be false.

Example: Intellectuals should be respected, and people's teachers are intellectuals, so people's teachers should be respected.

Among them, the main item in the conclusion is called the small term, which is represented by "s", such as "people's teacher" in the above example; The predicate in the conclusion is called the big term, which is denoted by "p", as in the example above, "should be respected"; The term common to the two premises is called the middle term and is denoted by "m", as in the example above, "intellectual".

In syllogisms, the premise that contains major items is called the major premise, as in the above example, "intellectuals should be respected"; The premise that contains a sub-item is called a minor premise, as in the above example, "the people's teacher is an intellectual". Syllogism reasoning.

Based on the relationship between the middle term m and the major term p and the small term s indicated by the two premises, the conclusion that the relationship between the small term s and the major term p is deduced through the mediating effect of the middle term m.

The so-called deductive reasoning.

It is the process of starting from a general premise and deriving a specific statement or individual conclusion through deduction, i.e. "deduction". There are also several definitions of deductive reasoning:

1. Deductive reasoning is reasoning from the general to the particular.

2. It is the reasoning of the conclusion implied by the premise.

3. It is reasoning that has a necessary connection between the premise and the conclusion.

4. Deductive reasoning means that there are sufficient conditions or sufficient necessary conditions between the premises and the conclusion.

The inevitability reasoning of the connection.

A logical form of deductive reasoning.

The significance of rationality lies in the fact that it has an irreplaceable corrective effect on the rigor and consistency of human thinking. This is because deductive reasoning guarantees that reasoning is valid not on the basis of its content, but on its form. The most typical and important applications of deductive reasoning are usually found in logical and mathematical proofs.

Specific examples of deductive reasoning are:

1. Premise: All metals can conduct electricity; Minor premise: Iron is a metal; Conclusion: So iron can conduct electricity.

2. The main premise: all natural numbers are integers; Minor premise: 4 is a natural number; Conclusion: So 4 is an integer.

3. Premise: The rectangle is a parallelogram; Minor premise: a triangle is not a parallelogram; Conclusion: So a triangle is not a rectangle.

4. The main premise: The shadow of the earth falling on the moon during the lunar eclipse is always round. Minor premise: Only spherical things can project a round shadow in any situation. Conclusion: So, this proves that the Earth is spherical.

5. The main premise: the sum of the three internal angles of any triangle is 180 degrees; Minor premise: A right triangle has a right angle with an angle of 90 degrees; Conclusion: So, the sum of the other two acute angles of a right triangle is 180 degrees - 90 degrees = 90 degrees.

6. Premise: If the last digit of a number is 0, then this number is divisible by 5; Minor premise: The last digit of this number is 0; Conclusion: So this number is divisible by 5.

7. Premise: If a figure is a square, then its four sides are equal; Minor premise: The four sides of this figure are not equal; Conclusion: It is not a square.