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Lecture notes, cheat sheets
Логика. Силлогизм (конспект лекций)
Directory / Lecture notes, cheat sheets Table of contents (expand) LECTURE No. 16. Syllogism 1. The concept of syllogism. Simple categorical syllogism The word "syllogism" comes from the Greek syllogysmos, which means "conclusion". It's obvious that syllogism - this is the derivation of a consequence, a conclusion from certain premises. A syllogism can be simple, compound, abbreviated, and compound abbreviated. A syllogism whose premises are categorical propositions is called, respectively, categorical. There are two premises in the syllogism. They contain three terms of the syllogism, denoted by the letters S, P and M. P is the greater term, S is the lesser, and M is the middle, connecting term. In other words, the term P is wider in scope (although narrower in content) than both M and S. The narrowest term in a syllogism is S. Moreover, the larger term contains the predicate of the judgment, the smaller one - its subject. S and P are related to each other by the middle concept (M). An example of a categorical syllogism. All boxers are athletes. This man is a boxer. This person is an athlete. The word "boxer" here is the middle term, the first premise is the major term, the second is the minor. To avoid mistakes, we note that this syllogism refers to a given, specific person, and not all people. Otherwise, of course, the second premise would be much broader in scope. A categorical syllogism has four forms, depending on the position of the middle term in its structure. In the first case, the major premise must be general, while the minor premise must be affirmative. The second form of the categorical syllogism gives a negative conclusion, and one of its premises is also negative. The larger concept, as in the first case, must be general. The conclusion of the third form must be private, the minor premise must be affirmative. The fourth form of categorical syllogisms is the most interesting. From such conclusions it is impossible to draw a generally affirmative conclusion, and there is a natural connection between the premises. So, if one of the premises is negative, the larger one should be general, while the smaller one should be general, if the larger one is affirmative. In order to avoid possible errors, when constructing categorical syllogisms, one should be guided by the rules of terms and premises. The rules of terms are as follows. Average term distribution (M). Means that the middle term, the connecting link, must be distributed in at least one of the other two terms - the greater or the lesser. If this rule is violated, the conclusion is false. Absence of unnecessary syllogism terms. Means that a categorical syllogism must contain only three terms - the terms S, M and P. Each term must be considered in only one meaning. Distribution in custody. In order to be distributed in the conclusion, the term must also be distributed in the premises of the syllogism. Parcel rules. 1. Impossibility of withdrawal from private parcels. That is, if both premises are private judgments, it is impossible to draw a conclusion from them. For example: Some cars are pickups. Some mechanisms are machines. No conclusion can be drawn from these premises. 2. Impossibility of inference from negative premises. Negative premises make it impossible to draw a conclusion. For example: People are not birds. Dogs are not people. Conclusion is not possible. 3. The next rule says that if one of the premises of the syllogism is particular, then its consequence will also be particular. For example: All boxers are athletes. Some people are boxers. Some people are athletes. 4. There is another rule that says that if only one of the premises of the syllogism is negative, the conclusion is possible, but it will also be negative. For example: All vacuum cleaners are household appliances. This technique is not household. This technique is not a vacuum cleaner. 2. Complex syllogism In thinking, we operate with concepts, judgments and conclusions, including syllogisms. Like judgments, a syllogism can be simple (discussed above) and complex. Of course, the word "difficult" should not be understood in the usual sense of the word, as "heavy" or "difficult". A complex syllogism consists of several simple syllogisms. They form polysyllogism, or complex syllogism; these are synonyms. A polysyllogism is a series of simple syllogisms connected to each other in a sequential manner. In this case, the conclusion, the consequence of one of the simple syllogisms becomes a premise for the subsequent one. Thus, a kind of “chain” of syllogisms is obtained. All polysyllogisms are divided into regressive и progressive. A progressive syllogism is characterized by the fact that its conclusion becomes the larger premise of the next syllogism. The conclusion of the regressive syllogism becomes the lesser premise in the following. 3. Abbreviated syllogism For ease of use and saving time, and especially in cases where the conclusion is obvious, abbreviated syllogisms are used. When talking about abbreviated syllogisms, it means that in such a conclusion one of the premises is missing, and in some cases the conclusion. All birds have wings. All seagulls are birds. All seagulls have wings. This is an example of a simple categorical syllogism. In order to get an abbreviated syllogism, you can omit the big premise, i.e. "all seagulls have wings." Thus, we get: "All seagulls are birds, which means that all seagulls have wings." Naturally, in this case the consequence of the syllogism will be true. In other words, the reduction of the syllogism does not affect its truth or falsity. You can give this example: "All gases are volatile, therefore, oxygen is volatile." This is an abbreviated syllogism, and the full one is expressed as follows. All gases are volatile. Oxygen is a gas. The oxygen is volatile. Unlike the previous example, the smaller premise is omitted here. The conclusion is skipped in the case when there is no need to express the result obtained due to its obviousness, obviousness for others, which stems from the nature of the premises themselves (i.e., if the premises and related objects, phenomena are well known). For example: "Everything that is lighter than water does not sink in it. Styrofoam is lighter than water." In this case, the omitted conclusion is fairly obvious. The syllogism looks like this. Anything lighter than water does not sink in it. Styrofoam is lighter than water. Styrofoam does not sink in water. In these cases, the restoration of the syllogism is quite simple, but sometimes there are problems with the definition of the premise and conclusion and their separation from each other. Therefore, it must be borne in mind that the words “because”, “because”, etc. are usually placed before the premise. Words such as “therefore” or “therefore” are usually put before the conclusion. Since the abbreviated syllogism is convenient and compact, it is used more often than full categorical syllogisms. The abbreviated categorical syllogism is also called enthymema. 4. Abbreviated compound syllogism Among compound abbreviated syllogisms, there are epicheirems и sorites. We should start with sorites, since their concept is used when considering the second type. Just like complex syllogisms, sorites can be progressive or regressive. Progressive sorites are obtained from progressive complex syllogisms, regressive ones - from regressive ones. As mentioned above, one of the premises of a complex syllogism is the conclusion of the previous one. When reducing a complex syllogism to the sorites form, this premise is omitted. The complex premise of the subsequent judgment in a polysyllogism may also be missed. The progressive sorite contains the predicate of the conclusion and its subject. It starts first and ends second. Unlike the progressive sorite, the regressive sorite begins not with the predicate of the conclusion, but with its subject. It ends with a predicate. Progressive sorites scheme. All A is B. All C is A. All D is C. All D is B. Regressive sorites diagram. All A is B. All B is C. All C is D. All A is D. Author: Shadrin D.A. << Back: Conclusion. General characteristics of deductive reasoning (The concept of inference. Deductive inferences. Conditional and disjunctive inferences) >> Forward: Induction. Concept, rules and types (The concept of induction. Rules of induction. Types of inductive inferences)
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