What does reasoning have to do with entailment? What is the difference between reasoning and inducti

Entailment is logic.

It plays a very important role in the development of logic. The concept of entailment has a long history of research, but logicians do not have a universally accepted answer to this question. Due to the different understandings and grasps of the meaning of entailment, logicians have proposed different concepts of entailment and constructed logical systems with different properties and functions.

Causal reasoning is one of the most commonly used forms of reasoning in everyday thinking.

Implication is to discuss the "truth transfer relationship between propositions and propositions", the difference between the two is the truth value relationship between propositions, the connection between the two, may be the formalization of the idea of conditional sentences, it is indeed difficult to distinguish them if they are in the context of daily life, but there is still a very clear distinction in logic.

That is, all reasoning can be expressed as an entailment according to the so-called conditional rule, that is, an entailment in the form of "premise-conclusion". When used for actual judgment, if you make a specific judgment on whether the reasoning is valid or not based on some simple and intuitive opinions of people's daily life, this judgment is quite vague and imprecise, and it is very likely to be wrong.

If the existence of a thing is based on objective laws, then the existence of other things that are not that thing is also based on objective laws. If the law that exists between the existence of the thing and other things that does not belong to the thing can be indicated, then it proves that if the thing that is set up exists objectively, there are also laws between the thing and other things.

Inference and entailment should be causal, whereas causal reasoning is an epistemological concept. This conceptual distinction and clarification, and the inconsistency of the causal relationship between things, make it impossible for us to intuitively come up with a recognized definition of entailment.

Reasoning, logic refers to one of the basic forms of thinking, which is the process of deriving new judgments (conclusions) from one or several known judgments (premises), including direct reasoning, indirect reasoning, etc.

There is no direct relationship between reasoning and entailment, indirect relationship, reasoning about a thing takes a little time, and entailment is its own existence.

Reasoning is based on the information contained in a thing or an object, so reasoning and entailment are a relationship between inclusion and containment.

Reasoning is to deduce certain facts according to certain objective conditions. And then what kind of meaning does this reasoning come out of?

Both may be formalizations of the idea of conditional sentences (if then), and each has its own characteristics that complement each other.

Inductive reasoning: Humans, horses, and mules are long-lived (premise), and these are all gutless animals (premise), so all gutless animals are sold for longevity (conclusion).

The main form of deductive reasoning is the "syllogism", which consists of three parts: the major premise, the small front Naweiti, 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.

The dialectical relationship between them is as follows: on the one hand, induction is the basis of deduction, and there is no deduction without induction; On the other hand, deduction is the precursor to induction, and without deduction there is no induction. All scientific truths are the product of the dialectical unity of induction and deduction, and neither deductive nor deductive deduction can reach scientific truth without deduction.

Induction is the basis of deduction. Deduction begins from where induction ends, and the general knowledge of deduction is the result of induction before experience. It is impossible to establish the law of conservation of energy without a large number of empirical facts of mechanical motion; Without the fact that there are a large number of experiments with biological hybridization, it is impossible to create the theory of inheritance.

The above information refers to the encyclopedia - induction and deduction.

An example of deductive reasoning is simply a syllogism:People die. Socrates was human.

So Socrates will also die.

Examples of inductive reasoning are simple:Swallows can fly. Orioles can fly.

Swans can fly. Red-crowned cranes can fly.

Main differences:The requirements for the authenticity of the premises are different. Deductive reasoning does not require that the premises must be true, whereas inductive reasoning requires that the premises must be true.

The range of knowledge asserted by the conclusions varies. The conclusion of deductive reasoning does not go beyond the knowledge assumed by the premise. In addition to complete inductive reasoning, the conclusions of Hu Li are beyond the scope of knowledge determined by the premise.

The degree of connection between premises and conclusions varies. 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 premise and the conclusion is probable, that is, the premise is true and the form of reasoning is correct, but it cannot necessarily lead to a true conclusion.

Deductive is a linear method of reasoning that ultimately aims to arrive at a conclusion that is derived from the logical word "therefore". In the pyramid structure, the idea that is located above the deductive argument process is a generalization of the deductive process, with emphasis on the final step of the deductive reasoning process, the conclusion that is drawn from the logical word "thus".

To put it simply, the deduction is divided into the following 3 steps:

1. All people will die (Explain the existence of a certain situation in the world.) ）

2. Socrates is man (expounding the relevant situations that exist at the same time in the world).

3. So Socrates will die (illustrating the implicit meaning of the simultaneous existence of these two conditions).

You should try to place deductive reasoning at a lower level in the pyramid structure, and try to minimize the insertion of other distracting information in the deductive reasoning process. The use of deductive methods in a certain paragraph is appropriate and easy for the reader to understand. However, at a higher level, inductive is always easier than deductive.

When connecting deductive reasoning, it is important to keep in mind that:

1. The process of deductive reasoning should not exceed 4 steps;

2 Do not derive more than two conclusions.

Inductive reasoning is the grouping of a group of facts, ideas, or opinions that have something in common and generalizing their commonalities (or arguments).

Here's the inductive reasoning:

1. Socrates died.

2. Plato died.

3. Therefore, people will pass away.

When it comes to thinking creatively with induction, we must have the following two main skills:

Define the group of ideas correctly.

Accurately identify and weed out ideas in the group that are out of proportion to the rest.

In the process of deduction, each thought is derived from the previous one; In the process of induction, there is no such relationship.

Mathematical Reasoning or Detective Reasoning?

Concept is the generalization and reflection of the essence of things, and the reflection of the common and general characteristics of similar things in the human brain.

Judgment is the determination and determination of what a thing is or is not, whether it has a certain attribute, is a reflection of the connection or relationship between things in terms of content, and is manifested in form as the connection between concept and function.

Reasoning is the thinking activity of deducing the unknown from the known from the connection or relationship of things, and its logical form is to deduce a new judgment from several known judgments, which is the manifestation of a certain connection or relationship between judgments.

Concept: Cognition of the position of words and phrases in a category system.

Judgment: Judgment is based on judgment and cognition of the ultimate abstract category.

Proposition: Use judgment to speak and recognize all sexual changes.

Definition: A proposition that confirms the connotation and extension of a concept.

Inference: Deducing or inducing a new proposition from a known proposition.

Deductive reasoningIt is a method of reasoning from the general to the particular, which is the process of starting from the general premise, through deduction, i.e., "deduction", to arrive at specific statements or individual conclusions.

Inductive reasoning: is a kind of reasoning 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 difference between deductive reasoning and inductive reasoningAnd here it is:

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 an inevitable thinking process. Deductive reasoning is not reasoning from the individual to the general, but it is not just reasoning from the general to the individual.

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

3. The scope of knowledge asserted by the conclusion is different: the conclusion of deductive reasoning does not exceed the scope of 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. Inductive reasoning is contingent except for the fact that the connection between the premises and the conclusion is inevitable in complete inductive reasoning.

The following one is copied back for reference:

Inductive and deductive methods are the study methods of logic.

Inductive method is a way of thinking and a form of reasoning that summarizes general principles from individual facts obtained from observation, experiment, and investigation, and its main link is inductive reasoning. Inductive reasoning can be divided into three ways: complete induction, simple enumeration, and inductive reasoning to determine causal connections.

The main functions of the inductive method are:

1. Guiding method of scientific experiments: In order to find causal relationships, the inductive method is used to arrange reproducible experiments.

The advantage of the inductive method is that the causal relationship is determined, and then the causal law is used as the objective basis for logical reasoning, and the observation, experiment, and investigation are used as means, so the conclusions are generally reliable.

Induction also has its limitations, it only deals with linear, simple and deterministic causal connections, and it is powerless for complex problems such as nonlinear causal connections, two-way causal connections and random causal connections.

Induction is a method of probabilistic reasoning, which cannot be completely inducted, and there are always many objects that are not included, so the conclusions are not necessarily reliable.

The deductive method, in contrast to the inductive method, is to deduce individual conclusions from general principles, and the main form of deductive reasoning is the syllogism, which consists of three parts: the major premise, the minor premise, and the conclusion.

The main effects of the deductive method are:

1. Test hypotheses and theories: The deductive method makes inferences about hypotheses, and uses observation and experiments to test hypotheses.

2. Tools for logical argumentation: provide logical proof for the rationality of scientific knowledge.

3. The means of making scientific predictions: apply a principle to specific occasions and make correct reasoning.

Deductive reasoning is a kind of necessary reasoning, the premise of reasoning is general, the conclusion deduced is individual, and the individual is generalized in general.

Things have commonality and must contain individuality, so the "individual" must be deduced from the "general", and whether the deduced conclusion is correct depends on whether the major premise is true and whether the reasoning is logical.

The deductive method also has its limitations, and the reliability of the inferential conclusion is constrained by the premise (the inductive conclusion), and whether the premise is correct or not cannot be solved within the scope of deduction.

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.

1. Deduction must be based on induction.

People first use the method of induction to generalize individual things into general principles, and then deduction can start from this general principle. Deduction is premised on the conclusion reached by induction, and there is no deduction without induction.

2. Induction must be guided by deduction.

When people collect empirical materials in preparation for induction, they must be guided by certain theoretical principles in order to collect them purposefully in a definite direction, otherwise they will lose their way.

3. Induction and deduction penetrate and transform each other.

In the process of thinking, induction and deduction are not absolutely separated, in the same thinking process, there are both induction and deduction, and induction and deduction are connected, interpenetrated, and transformed into each other.

Inductive reasoning is reasoning in which some objects of a certain class of things are deduced from the fact that all the objects of that class of things have these characteristics, that is, reasoning that generalizes general principles from individual facts.

Deductive reasoning is to start from general principles and deduce conclusions in a particular situation, that is, reasoning from the general to the particular. The pattern of deductive reasoning is the syllogism.

The step of inductive reasoning is to discover certain identical properties by observing individual situations, and then deduce a definite general proposition (conjecture) from these known identical properties; Deductive reasoning is a conclusion based on a major premise known general principle, a minor premise on a particular case studied, and a judgment about a particular case based on a general principle.

The conclusions obtained by inductive reasoning are not necessarily correct, and deductive reasoning will arrive at correct conclusions when the major premise, minor premise, and reasoning process are not wrong.