What are the types of premise argumentation of syllogism?

Syllogism reasoning is a simple reasoning judgment in deductive reasoning. It consists of three parts: a proposition (major premise) containing major terms and middle terms, a proposition (minor premise) containing minor terms and middle terms, and a proposition (conclusion) containing minor terms and major terms. In fact, syllogism is a process based on a general principle (major premise) and a special statement (minor premise) attached to the general principle, which leads to a special statement (conclusion) that conforms to the general principle. Syllogism is one of the scientific thinking methods that people can get correct conclusions when thinking about mathematical proof, case handling and scientific research. It is a form of correct thinking in deductive reasoning.

Syllogism reasoning is a simple reasoning judgment in deductive reasoning.

He includes: a general principle (major premise), a special statement attached to the previous major premise (minor premise), and a conclusion that the special statement conforms to the general principle.

Syllogism reasoning: When thinking, the brain first uses a well-defined and wide-ranging general principle A (referred to as' major premise'), and then finds another minor premise B through scientific experiments. When all the connotations of the concept of B can be contained in major premise A and described in words, it cannot be artificially the same as the content essence of major premise A (short for minor premise B). Then according to minor premise B, if it belongs to major premise A, then the nature of B must be the same as that of major premise, and a reliable and correct judgment can be obtained. This thinking process is called the correct conclusion C process-the scientific term is "syllogism reasoning".

Note: the new conclusion judged by this syllogism method can also be a new starting point for people to make a surprise study in the next step. In syllogism thinking, B must have a solid' argument', otherwise the conclusion C can be said to be wrong. Einstein's "theory of relativity" C also relies on syllogism reasoning. Any thinking that violates the principle of syllogism cannot get a reliable conclusion. It is easy to lead to the form of "circular argument": for example, "practice is the only criterion for testing truth", artificially changing "syllogism" into "two-paragraph theory" The mistake lies in the topic, that is, the argument, which is illegal to combine into one, and logically proves that the establishment is illegal.

Syllogism is one of the scientific thinking methods that people can get correct conclusions when thinking about mathematical proof, case handling and scientific research. It is a form of correct thinking in deductive reasoning.

Judging from the thinking process, any' syllogism' must have major and minor premises and conclusions, and no part can form syllogism reasoning. However, in specific language expressions, some parts of syllogism are often omitted, whether speaking or writing articles. But' not telling' does not mean' abolishing'. Because "major premise, minor premise and conclusion" cannot be omitted in principle.

Omit the major premise

You are a student of the School of Economics, so you should learn economic theory well.

Example 1 omits the premise that all students in the School of Economics should learn economic theory well.

Reform is a new thing, and it is inevitable to encounter difficulties in progress.

Example 2 omits the major premise: "Any new thing is bound to encounter difficulties in its progress".

Omit minor premise

All enterprises should improve their economic efficiency, and state-owned enterprises are no exception.

Example 1 omits the minor premise that "state-owned enterprises are also enterprises". Restoring its integrity means: "All enterprises should improve their economic benefits, and state-owned enterprises are also enterprises, so state-owned enterprises should improve their economic benefits".

This series is not an excellent work, because an excellent work is a combination of ideological and artistic works.

The minor premise of omission is that "this series is not a combination of ideological and artistic". Restoring its integrity means that "excellent works are works combining ideology and artistry, and this series is not works combining ideology and artistry, so this series is not excellent works".

Ellipsis conclusion

(1) Amateur education is popular among the masses, and correspondence education is one of the forms of amateur education.

The conclusion of omission is that "the form of correspondence education is welcomed by the masses".

Everyone makes mistakes, and you are human.

The conclusion of omission is "you can't avoid making mistakes"

It can be seen that in these four cases, the position of the subject and predicate in the conclusion (below) is fixed. The main difference between these grids lies in the different positions of items in the premise.

There are also some differences in isomorphic syllogism, that is, their premises and conclusions involve different quantifiers (full names and proper names) and properties (affirmation and negation), that is to say, their "forms" are different.

For example:

1, all cloven-hoofed animals are vertebrates, and cattle are cloven-hoofed animals; So cows are all vertebrates. (AAA style in the first box)

2. All cloven-hoofed animals are not insects, and cattle are cloven-hoofed animals; So cows are not insects. (the first case EAE style)

3, all goods are used for exchange, and all feudal land rent is not used for exchange; So all feudal land rent is not a commodity. (AEE type of the second grid)

4. Ostrich can't fly, ostrich is a bird; So some birds can't fly. (The third case EAO style)

5. Some flightless animals are ostriches and ostriches are birds; So some birds are flightless animals. (Type IAI of the fourth grid)

The possible and effective forms of syllogism;

In each lattice of syllogism, four judgments, A, E, I and O, can be used as major and minor premises and conclusions respectively, and the number of combinations is 4X4X4=64. So as far as its possibility is concerned, each cell has 64 formulas. There are four lattices in' syllogism', so there are 64X4=256 possible syllogism forms.

However, not all possible formulas of syllogism are valid. In fact, most of them are invalid.

For all possible forms of syllogism, whether it is valid or not can be judged according to general rules or specific rules of each situation. After screening, among all possible formulas of syllogism, * * * has the following 24 effective formulas.

The way to verify the correctness of syllogism is that a syllogism is valid and must be realized if and only if it is one of 24 formulas.

Among the above 24 valid expressions, there are 5 brackets, which are called weak expressions. The so-called weak form means' the full name conclusion could have been drawn, but only a special conclusion was drawn.' The weak form cannot be regarded as an independent valid form.

In this way, if not counting the five weak forms, there are 19' effective forms' in the syllogism * *.

We don't need to memorize the effective formulas of syllogism one by one. In fact, the validity of syllogism can be judged correctly according to the general rules of syllogism and the specific rules of each case.

Ellipsis of syllogism:

Syllogism includes three parts: major premise, minor premise and conclusion. Logically speaking, these three parts are indispensable. However, in the expression of daily language, syllogism can often be omitted.

A syllogism that omits a major premise or minor premise or conclusion in daily language expression is called an ellipsis syllogism, which can also be called an ellipsis syllogism.

The descriptive content of ellipsis syllogism is only a language expression, and its logical structure cannot be omitted. That is to say, the ellipsis of' ellipsis syllogism' is actually a necessary part of default reasoning in logical structure, but people don't express it in words. It's best not to omit the article in case others can't understand it.

There are three forms of ellipsis syllogism:

First, the major premise of ellipsis: the major premise of ellipsis, its content is often the universally recognized truth that human beings have obtained. For example, the sun rises in the east; Animals always die.

Second, omit the minor premise: the minor premise of omission is often a' self-evident fact'. (conclusive evidence)

Third, omit the conclusion: omit the conclusion, (if the conclusion is obvious and not easy to misunderstand, some people think that not saying the conclusion is often more powerful than saying it. But scientific research is not allowed to be vague. The conclusion drawn by "logical" thinking is not a literary work. Therefore, it is better not to omit the conclusion.

The recovery of ellipsis in syllogism;

The necessity and advantages of syllogism ellipsis have been mentioned above.

But syllogism ellipsis also has weaknesses. Some syllogisms with false premises or erroneous reasoning, after being omitted, are likely to cover up these defects and are not easy to be detected. Sophists often have these ways to fish in troubled waters in theory.

Therefore, when judging the validity of the ellipsis syllogism, we need them to add ellipsis first and restore the ellipsis syllogism to a classic and complete form.

The recovery of' ellipsis syllogism' has the following steps:

1, determine whether the conclusion is omitted? Before drawing a conclusion, we usually use conjunctions such as "therefore" and "so". According to whether there is such a conjunction, you can easily judge whether the conclusion has been omitted.

2. If the conclusion is not missed by others, then the major and minor events can be determined according to the conclusion. If there is no major item in the omitted premise, it means that the major premise is omitted; If the minor item does not appear in the premise, it is an omitted minor premise.

3. Add the omitted parts and arrange them properly, and you can get the complete form of' omitted syllogism'.

When resuming the ellipsis of syllogism, we should pay attention to two points:

First, we can't go against the original intention of omitting syllogism. Generally speaking, the content of the omitted part of the' ellipsis syllogism' can only be omitted if it is obvious to people. It should be restored according to the obvious original intention of' omitting syllogism'. We can't go against its original intention to' avoid omitting formal mistakes after the resumption of syllogism'.

Second, if there is ambiguity about the original intention of "omitting syllogism", then the judgment you added when you resumed should be true. If true judgment is not added as a premise or conclusion against the original intention, but false judgment is added wrongly, the significance of restoring' omitting syllogism' will be lost. It doesn't help at all.

The so-called' validity of reasoning' means thinking from the real premise (the connotation of seeking truth from facts) through reasoning, which is very important, because only in this way can we draw a truly reliable conclusion. If a form of reasoning derives a wrong conclusion from a "true premise", it is invalid. But sometimes people don't know that this is a wrong conclusion and think it is the truth.

In traditional logic, 24 of the 256 formulas of syllogism are valid, and all other formulas are invalid.

The first box: AAA, EAE, AII, EIO；; ; EAO AAI .

The second grid: AEE, EAE, AOO, EIO；; ; EAO AEO .

The third grid: AII, IAI, EIO OAO；; ; EAO AAI .

The fourth grid: AEE, IAI, EIO；; ; AEO，EAO，AAI .

Note: The semicolon is preceded by an unconditionally valid expression, and the semicolon is followed by a conditionally valid expression, which will be explained below.

Traditional logic assumes that the main item (minor item) of the conclusion is not empty, that is, the elements of the set represented by this item exist. This assumption ensures the validity of the nine formulas after the semicolon in the above four grids, and the validity of the formula 15 before the semicolon is not affected by this assumption. As you can see, the nine valid expressions after the semicolon all have one characteristic, that is, the conclusion is special, provided that the full name is given.

According to Boolean's point of view, the full-name proposition does not contain existence, that is to say,' proper name proposition cannot be deduced only from the full-name proposition' (generally speaking, proper name proposition is considered to have the meaning of existence, and "there is an A, and that A is B" means "there is an A"). For example, "all cars are vehicles" does not mean "cars exist", so he thinks that syllogism only has 15 valid expressions before semicolons.

Aristotle believes that when the subject actually exists, the full name proposition contains existence, but it is not. For example, "all cars are means of transportation" implies the existence of cars, while "all unicorns are animals with only one horn" does not imply the existence of unicorns, so he thinks that the nine formulas after semicolons are also valid when the events (namely "cars" and "unicorns" above) are not empty. We can also say that the 15 valid expressions before the semicolon are unconditionally valid, and the last 9 valid expressions are conditionally valid.

It is not difficult to see that the conclusion of the first effective formula contains four forms of AEIO, the second contains only two forms of negative E and O, and the third contains only two forms of special I and O. The conclusion of the first effective formula contains all forms of outspoken proposition, which is more in line with daily expression habits and therefore more important. As we can see later, the effective form of syllogism can be proved by the first four forms of the first case.

According to the axioms of syllogism, people summed up the general reasoning rules of syllogism, making it the standard to judge whether syllogism is effective or not. There are seven general rules in syllogism, of which the first four are basic rules and the last three are derived rules. Of these seven rules, the first three are about word items; The last four rules are about premises and conclusions.

The general rules are as follows:

(1) A correct syllogism has only three different terms.

The essence of syllogism is to use a * * * homonym item, that is, the middle term item, as an intermediary to make the big term and the small term have a logical relationship and draw a conclusion. If a syllogism has only two words or four words, then the size items can't find a related * * * identical item, so the relationship between the size items can't be determined. Therefore, a correct syllogism only allows three different terms.

If there are only two words (A is B, so B is A), it will lead to meaningless repetition of the same word, and no new conclusion can be drawn. You can't make a logical mistake of "four words" (A is B; C is d, so a is d);

(2) The middle term of syllogism should be GAI at least once. (To avoid logical errors)

The middle term is the medium connecting the major premise and the minor premise. If there is no GAI in the' premise' once, then some extensions of the middle term will be associated with big words and some extensions will be associated with small words, so the relationship between big words and small words cannot be determined.

We can't let GAI fail twice on the major premise and minor premise. What if the item is in GAI once or twice on the premise of size? If the middle term is GAI once, there will be a positive or negative correlation between all the extensions of the middle term and the major or minor terms, which will produce a media effect and make the relevant size premise reach an inevitable conclusion.

Examples of correct thinking:

(1) Intellectual B belongs to laborer A (in a larger scope), and Professor Li T is an intellectual B, so Professor Li T belongs to laborer A. ..

② Intellectual B is not an exploiter Z, and Professor Li T is an intellectual B, so Professor Li T is not an exploiter.

③ Every actor D has motive H, while someone W has no motive D; So someone d is not motive H.

In all the above examples, only one item is GAI, and all of them can draw an inevitable conclusion. The relationship between major premise and minor premise and conclusion is inevitable.

If the lexical item GAI is twice, as long as the premise of size is not completely negative, then all the extensions of lexical items will be connected with events and events respectively, which will play the role of connecting large and small items, thus making syllogism draw an inevitable conclusion.

In a word, a correct syllogism (as long as both premises are not negative) should have a middle term of GAI at least once.

(3) If it is not GAI in the premise, it is not GAI in the conclusion.

This rule is the same as the direct transposition reasoning rule of nature judgment. If the events or events in the premise are not GAI, then their events or their extensions are not completely determined. If the event or event in the conclusion becomes GAI's, it is equivalent to determining the extension of the event or event. This is inconsistent, the conclusion is certainly unreliable, and its conclusion is not necessarily derived from the premise. In violation of this rule, the logical error committed is called "improper expansion of major events" or "improper expansion of minor events"

Example: [Note that the connotation of A is greater than that of B, for example, A includes B, C, D, E, ...]

(1) Advanced workers B are all people who get an A in their work, and Lao Wang is not an advanced worker B, so Lao Wang is not a person who gets achievements in his work. (error)

(2) Metal B is conductor A and rubber is not metal B, so rubber is not conductor A .. (Error)

(3) Metal B is an electrical conductor A, and metal B is not an insulator E, so all insulators E are not electrical conductors. (right)

(4) Someone A is a professor B and someone A is a Peking University C, so everyone in Peking University is a professor. (Wrong) (The concepts of location and location are different)

The logical mistake made in the above example 12③ is "improper expansion of major events". The logical mistake made in Example 4 is "improper expansion of events". From the above example, the conclusion is false and true, which shows that the conclusion derived from violating this law is unreliable, that is, the conclusion derived from the premise is not inevitable, but probable. Examples 2 and 3 cannot be regarded as effective reasoning just because such reasoning can lead to a true conclusion. The form of reasoning that can come to a true conclusion by accident is invalid. Any logical form of effective reasoning, as long as the premise is true, can certainly draw a true conclusion if it is substituted into any reasoning content.

(4) Two negative premises cannot lead to a conclusion.

If both premises are negative, then the middle term is excluded from the major and minor terms. In this way, the term can't play the role of the premise of link size, and the relationship between the minor term and the major term can't be determined, so it is impossible to draw a conclusion. Here are two examples to illustrate this rule.

① Copper (M) is not an insulator (P) and iron (S) is not copper (M), so iron (S) is not an insulator (P).

② Sheep (M) is not a carnivore (P) and tiger (S) is not a sheep (M), so tiger (S) is not a carnivore (P).

In the above two cases, the premise is true, but the conclusion is probable because the form is invalid.

(5) If a premise is negative, its conclusion must be negative; If the conclusion is negative, then one of the premises must be negative.

This rule is an export rule. If the major premise of a syllogism is negative, then the extension of the middle term and the big term must be mutually exclusive. According to Rule (4), "Two negative premises cannot reach a conclusion, so the minor premise can only be positive. If the minor premise is affirmative, then there must be a compatible relationship between the extension of the middle term and the minor term in the minor premise. In this way, through the intermediary role of the middle term, the small term will be excluded by the extension of the big term, thus reaching an inevitable conclusion. Similarly, if the minor premise is negative, then the extension of the middle term and the minor term is mutually exclusive; According to Rule (4), the major premise can only be affirmative, so the extension of Chinese words and big words must be compatible.

From another point of view, if the premises are all positive and the conclusion is negative, then the relationship between minor and major in the conclusion is either true inclusion, cross-correlation or completely different, but in fact the premise of positive size is connected by items, and the extension relationship between minor and major may be the same, true inclusion, true inclusion or cross-correlation, so that the relationship between minor and major contained in the premise is the same.

(6) Two special premises cannot be concluded.

If both premises are special judgments, then syllogism has four combinations of * * *. Namely II, OO, IO, OI. The following are analyzed separately.

If both premises are of the second kind, then the subject and predicate in both premises are not GAI. In this way, no matter whether the middle term is located in the subject or predicate of two premises, it can't be GAI, which is bound to violate rule (2) and its reasoning form is invalid.

If both premises are OO, rule (4) is violated. Therefore, its reasoning form is also invalid.

If both premises are IO types, rule (3) is violated. Because the event, whether it is the subject or predicate of I judgment, can't be GAI, and according to rule (5), the conclusion should be negative, so the event of conclusion is GAI, which will definitely violate rule (3) and its reasoning formula is invalid.

Rule (2) or rule (3) is violated if the two premises are OI types. If the middle term is the subject of the major premise O judgment, and the middle term in the minor premise is either the subject or the predicate, then neither middle term in the major premise nor the minor premise is GAI, which will inevitably violate rule (2). If the major term P is the major term judged by the major premise O, the conclusion must be negative according to rule (5), so the major term P is not GAI in the major premise but GAI in the conclusion, which will inevitably violate rule (3). It is best to find an easy-to-understand metaphor to judge the above understanding through the relationship between' table, bowl and dish'.

Therefore, if the size premise is special, (understanding, the concept scope is too small to be deduced) will be invalid.

(7) One of the premises is special, and the conclusion must also be special.

According to rule (6), two special premises cannot be concluded, so if one premise of a correct syllogism is special, the other premise must be full name. So there is a premise called syllogism, and its combination of big and small premises has four types and eight forms:

AI - IA AO - OA EI - IE EO - OE

"EO-OE" in the above four groups can be directly excluded, because both premises are negative and violate rule (4), so only three groups can be analyzed.

If the size premise is composed of AI, no matter which one of them is the size premise, then their GAI item is only a subject of judgment. In order to abide by rule (2), the middle word must be in the subject of a judgment, so that the big and small words are in the predicate of a judgment and the subject-predicate of I judgment, and neither of them is GAI. In this case, GAI, the secondary term of the conclusion, will violate rule (3). Therefore, the minor terms of the conclusion of syllogism based on artificial intelligence can only be called special terms.

If the major premise and minor premise are both composed of AO, then no matter which one of them is the major premise and minor premise, their GAI items have a subject of judgment and a predicate of O judgment. According to rule (5), the conclusion can only be a negative judgment. If the conclusion is negative, the event in the conclusion is GAI. In order to comply with rule (3), events can only judge the position of subject or predicate in A or O, while in order to comply with rule (2), the middle term can only judge the position of subject or predicate in A or O.. In this way, events can only be judged in non-GAI items, that is, predicates or O.

If the size premise is IE, then, because the major premise I is not GAI, according to rule (5), its conclusion can only be negative judgment, that is, the event is GAI in the conclusion, so as long as the event is in the position where I judge the subject or predicate, it will inevitably violate rule (3), so IE as a premise cannot be established. If the premise of size is EI, then its GAI item has e to judge the subject and predicate. In order not to violate rule (2), the middle word is guaranteed to be GAI once, and in order not to violate rule (3), the big word is guaranteed not to expand in the conclusion, and the small word can only be located in the subject or predicate of I judgment. In this way, if the second term of the conclusion is GAI's, it will violate rule (3). Therefore, under the premise of EI, its conclusion can only be a special judgment.

I hope it can help you solve the problem.