In mathematics, what is deductive reasoning, trouble to illustrate with examples

Deductive reasoning is a three-step process.

The big premise, the minor premise, the conclusion.

The main premise is the general principle (law), that is, the abstraction of the general, unified results; The minor premise refers to the individual object, which is the reasoning from the general to the individual, from which the reasoning is followed and then the conclusion is drawn.

If you want to give an example, don't you understand the concept?

It's actually quite simple. Let's take a less refined example.

The premise - general principle - Class 1 is all boys.

Minor premise - individual object - you are also in class 1.

Conclusion – You're a man too.

That's it, o(o

Isn't the first floor too professional? It's actually very simple, for example: because everyone has to eat, and because I'm human, I'm going to eat.

The first two "because" are the premise (divided into major premise and minor premise), the second "so" is the conclusion, and the deductive reasoning from the premise to the conclusion is deductive reasoning. As long as the major premise, minor premise, and deductive reasoning norms are correct, the conclusion must be correct, from the surface to the point, which is also the most different from logical reasoning (logical reasoning is from the point to the surface).

Deductive reasoning is a method of reasoning from general to specific.

As opposed to "induction". The connection between the inferential premise and the conclusion is inevitable and is a kind of confirmatory reasoning.

To apply this method to study problems, we must first correctly grasp the general principles and principles that are the guiding ideology or basis; secondly, it is necessary to have a comprehensive understanding of the actual situation and particularity of the topic and problem to be studied; Only then can a conclusion be deduced that the general principles are used for a particular thing.

The forms of deductive reasoning include syllogism, hypothetical reasoning, and selective reasoning. In the educational work, the design and conduct of education and teaching experiments according to certain scientific principles of Jian Yancha are inseparable from this method.

The so-called deductive reasoning is the process of starting from the general pre-jujube cavity, and through deduction, that is, "deduction", to arrive at specific statements or individual conclusions. There are also several definitions of deductive reasoning:

Deductive reasoning is reasoning from the general to the particular;

It is the reasoning that the premise implies the conclusion;

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

Deductive reasoning is the reasoning of necessity that has sufficient conditions or sufficient necessary conditions between the premises and the conclusion.

The importance of the logical form of deductive reasoning to 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.

Deductive and inductive methods are considered to be the two most important methods of reasoning in rational thinking.

The so-called deductive method or deductive reasoning refers to the way in which people deduce the unknown part of things from the known part of the understanding on the basis of a certain theoretical understanding that reflects the objective law. It is a method of understanding from the general to the individual. The deductive method is the method of recognizing "tacit" knowledge.

The so-called inductive method or equilibrium and inference is the method of thinking used in the process of understanding things. Sometimes called inductive logic refers to a cognitive method in which people find out the basic laws or common laws that they obey based on a series of empirical things or knowledge materials, and assume that other things in the same kind of things also obey these laws, so as to use these laws as the basis for other things of the same kind to stop the principle of corruption.

It is "a conclusion, an inference that can be drawn from a known fact called a premise," and a necessary "conclusion." If the premise is true, the conclusion must be true. This is different from retrospective reasoning and inductive reasoning, which can presuppose a high-probability conclusion, but do not ensure that the conclusion is true.

"Deductive reasoning" can also be defined as reasoning in which the conclusion is not more universal than the premise, or "the conclusion is as certain as the premise".

Deductive reasoning, also known as syllogistic reasoning, is composed of two premises and a conclusion, the main premise is the general principle (law), that is, the abstract derivation of general, unified results; The old and small premise refers to individual objects, which is reasoning from the general to the individual, from which the reasoning is followed by a conclusion. It is also known as reasoning from law to phenomenon. It is from the ordinary to the special and then to the individual.

Deductive reasoning is correct for the lease conditions: if the major and minor premises are correct, then the conclusion is correct; If the major or minor premise is wrong, the conclusion is wrong.

Induction and deduction are two ways of logical thinking in the writing process. Human cognitive activities always come into contact with individual things first, then push to the general, and then from the general to the individual, and so on, so that the understanding is constantly deepened. Induction is to go from the individual to the general, and deduction is to go from the general to the individual.

Induction and deduction are the most widely used logical thinking methods in scientific research. Marxist epistemology holds that all scientific research must apply inductive and deductive logical thinking methods.

The main form of deductive reasoning is the "syllogism", which consists of three parts: the major premise, the minor premise, and the conclusion. The premise is the general principle that is known; The minor premise is the special occasion of the study; The conclusion is a new knowledge that is derived by subsuming special occasions under general principles. For example:

The main premise: the current rental and sale is formed by the movement of electrons in a certain direction.

Minor premise; The free electrons of a metal can move in a directional manner under the action of an electric field.

Conclusion: So, metals can conduct electricity.

Summary. Hello, the difference between inductive and deductive reasoning is as follows

1. The thinking process is different. The thinking process of inductive reasoning is from the individual to the general, while the thinking process of deductive reasoning is not from the individual to the general, but is a thinking process that is necessarily derived.

2. The requirements for the authenticity of the premise are different. Deductive reasoning requires a major premise, and a minor premise must be true. Inductive reasoning does not have this requirement.

3. The scope of knowledge asserted in the conclusion is different. The conclusion of deductive reasoning does not go beyond the knowledge assumed by the premise. In addition to complete inductive reasoning, the conclusions of inductive reasoning are beyond the scope of knowledge assumed by the premise.

4. The degree of connection between the premise and the conclusion is different. The connection between the premise and the conclusion of deductive reasoning is inevitable, that is, if the premise is true and the form of reasoning is correct, the conclusion must be true. In addition to the fact that the connection between the premises and the conclusion of complete inductive reasoning is inevitable, the connection between the premises and the conclusion is contingent, that is, the premise is true and the form of reasoning is correct, but it cannot necessarily lead to a true conclusion.

The dialectical relationship between inductive and deductive methods in epistemology: the inductive method is from knowing the individual to knowing the general; The deductive method is to know the general and then to the individual.

That's my answer, thank you

The difference and connection between inductive reasoning and deductive reasoning.

Hello, the differences between inductive and deductive reasoning are as follows: 1. The thinking process is different. The thinking process of inductive reasoning is from the individual to the general, while the thinking process of deductive reasoning is not from the individual to the wild, but is an inevitable thinking process. 2. The requirements for the authenticity of the premise are different.

Deductive reasoning code silver requires a major premise, and a minor premise must be true. Inductive reasoning does not have this requirement. 3. The scope of knowledge asserted in the conclusion is different.

The conclusion of deductive reasoning does not go beyond the knowledge assumed by the premise. Inductive reasoning excludes the example of complete inductive reasoning, and the conclusions are beyond the scope of knowledge assumed by the premise. 4. The degree of connection between the premise and the conclusion is different.

The connection between the premise and the conclusion of deductive reasoning is inevitable, that is, if the premise is true and the form of reasoning is correct, the conclusion must be true. In addition to the fact that the connection between the premises and the conclusion of complete inductive reasoning is inevitable, the connection between the premises and the conclusion is contingent, that is, the premise is true and the form of reasoning is correct, but it cannot necessarily lead to a true conclusion. The dialectical relationship between inductive and deductive methods in epistemology:

The inductive method is from knowing the individual to knowing the general; The deductive method is to know the general and then to the individual. That's my answer, thank you

The application of word selection judgment in thinking practice.

Linguistic judgment has a great application in practice, for example, in the interrogation of a crime or in some pedagogical communication.