Definition of syllogism >:> The so-called syllogism refers to the reasoning that a homonym connects two outspoken propositions as the premise and draws a new outspoken proposition as the conclusion. A syllogism consists of three straightforward propositions, two of which are premises and one is conclusion. The major item of the conclusion is the minor item (represented by S), and the premise of including the minor item is the minor premise; The predicate of the conclusion is the major term (expressed by P), and the premise of including the major term is the major premise; Two premises * * * Some terms are called neutral terms (denoted by m). For example, all truths are correct; Darwin's theory of evolution is truth; Therefore, Darwin's theory of evolution is correct. This is a syllogism. Its two premises contain the same word "truth", and with this word as the intermediary, it links the two propositions of "all truth is correct" and "Darwin's theory of evolution is truth", and deduces the conclusion that "Darwin's theory of evolution is correct". In this syllogism, "right" is the major term (P), "truth" is the middle term (M) and "Darwinian evolution" is the minor term (S). General rules of syllogism >:> In order to make syllogism effective, we must abide by general rules. There are seven general rules of syllogism: Rule 1: In a syllogism, there can only be three different terms. In fact, syllogism is the relationship between the middle term (M) and the big term (P) and the small term (S) respectively, so as to draw a conclusion about the relationship between the small term and the big term. If there is no middle term, you can't draw a conclusion. It is in this sense that we say that terminology is a bridge or medium that connects big things and small things. Only when three concepts appear twice can three propositions be formed. More or less than three concepts cannot form three propositions or cannot form three propositions. The common "four mistakes", or "four conceptual mistakes", is that the words as middle items in the major and minor premises look the same, but they express two different concepts, so this syllogism actually contains four different items. Strictly speaking, there is no middle term, and there is no bridge and medium connecting big terms and small terms, so the conclusion is not inevitable. This kind of error is called "four-word item error" or "four-concept error". Rule 2: In the premise, the intermediate item must be GAI at least once. With the help of the bridge and media in the premise, syllogism draws the conclusion that at least one of the big events and small events has something to do with all the events, and the other has something to do with some or all of the events, thus ensuring a certain relationship between the big events and small events. Otherwise, both events are related to only one part of the middle term, so it is possible that the event is related to this part of the middle term and the event is related to another part of the middle term. As a result, there is no relationship between events, and it is impossible to draw an inevitable conclusion. The logical mistake made in violation of this rule is called "the item failed to GAI twice". Look at the following syllogism: professors are all teachers; Xiao Zhang is a teacher; So, (). This syllogism can't reach a definite conclusion. The reason is that "teacher", as a Chinese word, does not cover it once in the premise (in both premises, only "professor" and "Xiao Zhang" are part of "teacher"), so it is impossible to determine the relationship between "Xiao Zhang" and "professor" and draw an inevitable conclusion. If you violate this rule, you will make the mistake of "the item is not GAI", which is illogical. Rule 3: Items that are not GAI in the premise are not GAI in the conclusion. The logical mistake made in violation of this rule is "GAI's inappropriateness", which is embodied in two forms: "GAI's inappropriateness in small matters" and "GAI's inappropriateness in big matters". For example, cherry blossoms are plants; Lilacs are not cherry blossoms; Therefore, lilacs are not plants. In this syllogism, the event "planted" is not GAI's premise, but GAI made the mistake of "improper GAI event" or "improper expansion event" in his conclusion. Rule 4: No clear conclusion can be drawn from two negative premises. If the two premises are negative, it means that events and events do not intersect with at least part or all of the Chinese term, so there is no guarantee that events and events will be related to each other because they intersect with the same part of the Chinese term, and the Chinese term will not act as a bridge between events, so events and events themselves may be various relationships, so a definite conclusion cannot be drawn. Rule 5: ① If one of the two premises is negative, then the conclusion is negative. If one of the two premises is negative, according to rule 4, the other premise must be positive, that is to say, one of the big and small items has a positive connection with the middle term and the other has a negative connection with the middle term. Therefore, the connection between the part with positive connection to the project and the part with negative connection to the project must be qualitative or non-qualitative, and the conclusion must be negative. For example, all theists are not materialists; Some people are theists; Therefore, some people are not materialists. In this reasoning, the premise is negative, so the conclusion is negative. Then, why is the conclusion negative and one of the preconditions must be negative? This is because, if the conclusion is negative, it must be because one of the large and small items in the premise is combined with the middle term, while the other item is excluded from the middle term. In this way, the premise of the mutual exclusion between the major term or minor term and the middle term is negative, so if the conclusion is negative, one of the prerequisites must be negative. On the other hand, if the conclusion is negative, it means that the inclusion relationship is denied. But the positive premise reflects the inclusion relationship, so we can't deduce the negative conclusion from the two positive premises. In other words, two positive premises cannot get a negative conclusion. (2) if the conclusion is negative, then there must be a premise is negative. Since the conclusion is negative, there is a negative connection between the major item and the minor item, and this connection is established through the intermediary of the middle item, so one of these two items must be positively related to the middle item and the other is negatively related to the middle item. Therefore, one of the premises must be negative. No negative conclusion can be drawn from two positive premises. In other words, two positive premises cannot get a negative conclusion. For example, some animals are mammals; Mammals are viviparous animals; So some viviparous animals are not mammals. This example violates this law and draws a negative conclusion from two positive premises, so it is incorrect reasoning. Rule 6: You can't draw conclusions from two special premises. Rule 7: If one of the two premises has a special name, then the conclusion must be special. The ellipsis form of syllogism >:> The ellipsis form of syllogism is a syllogism that omits a premise or conclusion. For example, "you are a study Committee member and should be among the best." This is the omission of syllogism, omitting the major premise that "the study committee should be among the best". Omitting syllogism can also be omitting minor premises or conclusions. Due to the omission of a part of syllogism, it is easy to hide all kinds of logical errors if it is used improperly. For example, someone said, "I'm not a translator. I don't need to learn a foreign language well. " This is an ellipsis syllogism that hides logical errors. When the omitted part is added, the error can be clearly seen. The complete form of this syllogism is: "Anyone who is a translator needs to learn a foreign language well. I am not a translator, so I don't need to learn a foreign language well. " This syllogism is obviously wrong, because it violates the rule that "minor premise must be affirmative proposition", thus making a logical mistake of "improper expansion of major terms" in the conclusion. Sometimes it is necessary to supplement the omitted syllogism into a complete syllogism, and then see whether its premise is established and whether the reasoning process is effective. The effective test method is to supplement the omitted part and restore it to a complete syllogism. The supplementary process and procedure are: first, determine which proposition in the omitted syllogism is the conclusion. This can generally be judged according to the language symbol of the sentence expressing the proposition (the proposition after "because" is the premise and the proposition after "so" is the conclusion) or the contextual connection. Of course, if you still can't find a conclusion according to the above method, then it is likely to omit the syllogism omitted from the conclusion. Then, find the major premise or minor premise. Conclusion Once determined, according to the definition of syllogism structure, the concept of subject, predicate, middle term and the composition of proposition can be determined as the premise of size. The third step is to revert to a complete syllogism according to a certain syllogism format. After doing this work, we can check whether these inferences are correct according to the rules of syllogism. Detailed examples >> Example 1 All Hunan migrant workers in Beijing have applied for temporary residence permits; Those who have applied for temporary residence permits have obtained employment permits; Some migrant workers from Hunan came to Beijing as doormen; Some amateur martial arts school students have also become doormen; None of the students in amateur martial arts schools have obtained employment permits. If all the above conclusions are true, which of the following conclusions must be true? () A. Hunan migrant workers in Beijing have obtained employment certificates. B. None of the students in the amateur martial arts school have applied for a temporary residence permit. C. Some migrant workers from Hunan come to Beijing, and some are students from amateur martial arts schools. Some doormen do not have employment permits. The correct answer to this question is C, and syllogism is needed to solve this problem. From the first two sentences in the stem, option A can be deduced by syllogism, that is, "all migrant workers in Beijing and Hunan have obtained employment certificates". From the last sentence and stem of A, we can draw the conclusion that "the students in amateur Wushu schools are not migrant workers from Hunan to Beijing", so any migrant workers from Hunan to Beijing can't be students in amateur Wushu schools. That is, item C must be false. Option BD can be deduced step by step from the given conditions. Therefore, the correct answer is C. Comments skillfully use syllogism rules for reasoning. Some economists are graduates of university mathematics departments. Therefore, the graduates of some universities' mathematics departments are people who are very good at business management. Which of the following, if true, can guarantee the correctness of the above statement? () A. Some economists specialize in a certain field of economics and have little research on enterprise management. B. Some economists who are very good at business management are not graduates of the University Mathematics Department. C. economists are good at business management. D. All economists are good at business management. The correct answer to this question is d, and the reasoning of this question can be regarded as omitting syllogism. To ensure that reasoning is established, it is necessary to ensure that the minor premise of omission is true. Then, by analyzing the above figure, we will find that only by ensuring that all "economists" belong to "people who study business management" can we ensure that some or part of "university mathematics graduates" become "people who study business management". It can be seen that the minor premise of omission is the picture we see in the above picture. The category of "people who study business management" needs to include the category of "economists" in order to make the title effective. Comment on the omitted syllogism, supplement it appropriately when doing the problem, and learn to reason in the form of chart (Euler diagram). Of course, if you directly use the syllogism reasoning rules to push backwards, you can also get the answer quickly. For example, according to the minor premise and conclusion, we can know that the major premise is composed as follows: ① affirmative proposition (because minor premise and conclusion are not negative propositions); Item (2) is an economist (because this concept does not appear in the conclusion); (3) The item in the major premise must be GAI (because the item in the minor premise is not GAI), so it can be concluded that the major premise must be D. Smart people are short-sighted and I am short-sighted, so I am smart. Which of the following accords with the logical structure of the above reasoning? () A. I am a fool, because smart people are nearsighted, and my eyesight is so good. All pigs have four legs, but this animal has eight legs, so it is not a pig. Xiao Chen is very happy, so Xiao Chen must be very fat. Because happy people get fat. D. All chickens have sharp mouths, and this bird that has been in the tree has a sharp mouth, so it is a chicken. By decomposing the Euler diagram of stem, it is found that only item D conforms to the syllogism reasoning structure of stem. The chicken in this item is similar to the wise man in the stalk, the sharp mouth is similar to myopia, and the bird is similar to me, so their structures are similar. The answer should be item D. Comment on the question type of syllogism reasoning, we can solve the problem in the form of a graph, that is, draw a graph according to the extended relationship of concepts and express it in the form of a graph. If we judge according to the rules of syllogism, we can see that the middle item is not GAI, and so is item D. Xiang Jun: Because Kornas is an excellent athlete, he is eligible to join the celebrity club. Guofeng: But because Kornas smokes, he is not a good role model for young people. Therefore, Cornus officinalis should not be accepted by celebrity clubs. Which of the following is the premise of the national wind argument? Some excellent athletes smoke. Not all smokers are good role models for young people. All those accepted by celebrity clubs are good examples for young people. A. Only Ⅰ B. Only Ⅱ C. Only Ⅱ D. Only Ⅱ and Ⅲ analyze this problem. The correct answer is D, and the argument of national style includes two inferences. One inference is that "Cornus officinalis is not a good example for young people" from "Cornus officinalis smoking", and adding option 2 as a premise here can form an effective syllogism. Another reasoning is that "Cornus officinalis is not a good role model for young people" and that "Cornus officinalis should not be accepted by celebrity clubs". Adding option III as the antecedent here can form an effective syllogism. There is no need to assume option I as the premise of the national wind argument. Comment on the supplementary options to form an effective syllogism.