Direct Inference of Deductive Inference

Let's start with the conclusion. Important knowledge points in this chapter:

The relationship between basic propositions in traditional logic (Aristotle's logic)

Pay attention to two conditions

1) must conform to the existence hypothesis, that is, the class involved in the preset is not empty.

2) When considering the antagonistic relationship and the subordinate antagonistic relationship, the proposition must be even.

It can't be true (or false), otherwise it can't be false (true).

Inevitably true (false) means logically and mathematically true (false), for example, all triangles are triangles and all squares are circles.

Transposition method and mass exchange method can be understood by introducing examples. Transposition is the first two operations. Take the first A to A of transposition method as an example. First from a to e in the quality law, then from e to e in the transposition law, and then from e to a in the quality law.

The proposition on the left of the above table implies the proposition on the right. That is, if the left side is true, the right side must be true; The right side is fake, and the left side must be fake. Other circumstances cannot be inferred.

There are many problems in the existence hypothesis of traditional logic. George boole developed modern logic and put forward Boolean explanation.

The core of Boolean explanation is:

In practical application, if the principal term is not empty, you can look at the square matrix, if it is empty, you can look at the Boolean explanation.

John venn (1834- 1923), a British mathematician and logician, first expressed the standard outspoken proposition graphically.

Slash mark is empty, X mark exists, and there is at least one element.

Venn diagram played an important role in the later outspoken syllogism.

Aristotle's traditional logic discusses all straightforward propositions. An outspoken proposition is to discuss classes or categories, and to affirm or deny that one class is totally or partially contained in another class. (literally translated as "classification proposition" is not good! ! ! )

AEIO is a standard outspoken proposition.

A: all s are p.

E: no, s is p.

I: yes, s is p.

O: there is an s without a p.

Direct inference: To infer from a premise

Indirect inference: Inference from at least two premises.

In the first article, I said that the concept of deductive part is at least 10 level in the tree structure. Let me show you the beginning of this article.

A standard outspoken proposition consists of quantifier)+subject item)+copula)+predicate item.

Quantity items: all, none, part; Associated Items: Yes,No..

The composition of the standard outspoken proposition is 1 layer.

According to the function, there are concepts of quality, quantity and GAI.

Quality: Yes or No?

Quantity: General or Special?

GAI needs a good explanation.

GAI refers to the characteristics that describe the relationship between a proposition and its terms (that is, subject or predicate). When the proposition mentions every member of the class involved in the project, we say that the project belongs to GAI. (GAI's translation is really powerless. Literally translated as "distribution" is not good! ! ! )

Proposal A: All senators are citizens. The proposal discusses all senators, but not all citizens. Therefore, the subject of proposition A is GAI and the predicate is not GAI.

E proposition: No athlete is a vegetarian. The proposition discusses all athletes, and this category is excluded from the quality category. It also discusses that vegetarians are excluded from athletes. Therefore, the subject and predicate of e proposition are GAI.

I propose that some soldiers are cowards. The subject and predicate of I proposition are not GAI.

O proposition: Some soldiers are not cowards. Cowards are excluded from the specific category of "some soldiers". Every member of cowards can't be found in this group of "some soldiers". When a class is excluded from a class, we say that every member of this class has been mentioned. The subject of the o proposition is not GAI, but GAI. (I don't know much here)

According to the classification of features, this is the second floor. With the second floor, you can play the game of transposition and qualitative change. The transposition position is calculated on the basis of transposition and transposition, which is the third layer.

I and o propositions have existential significance. Some soldiers are cowards. There must be at least one soldier. He is a coward. Some soldiers are not cowards. There must be at least one soldier. He is not a coward.

In traditional logic, the I and O propositions are derived from the A and E propositions, so the A and E propositions must also be meaningful. But when the subject of a full-name proposition (such as proposition A) does not exist, it is empty, A and O will be false, so the contradiction does not exist.

For example, all Martians are blond. Some Martians are not blond. When Martians did not exist, these two propositions were the same.

In order to save the traditional logical phalanx, it is assumed that all classes involved in the outspoken proposition are not empty.

But this presupposition is problematic. First, it can't discuss empty classes. Secondly, theories in scientific research often involve empty classes. Therefore, logician Boolean developed modern logic and put forward Boolean explanation.

John bull (18 15- 1864). British logician and mathematician. One of the founders of modern symbolic logic.

Boolean explanation:

When it is impossible to infer directly, look at the contradictory proposition of the original proposition or try to deduce the original proposition from a proposition.

When the original proposition is false, its contradictory proposition must be true. Then we can see the relationship with a proposition through the difference relationship and qualitative change solution between contradictory propositions. (Can you deduce a proposition? )

According to "the upper layer implies the lower layer." That is, the upper layer is true, and the lower layer must be true; The lower position is false, and the upper position must be false. " And the proposition on the left side of the replacement bitmap implies the proposition on the right side. That is, if the left side is true, the right side must be true; The right side is fake, and the left side must be fake. "

If the original proposition is a subordinate proposition of a proposition, then a proposition is false. If a proposition can be deduced from the original proposition by changing its position, then it can be concluded that a proposition is false because the original proposition is false.