The general rules of syllogism and logical figures make it easy to distinguish correct conclusions from wrong ones. If in the process of mental analysis it turns out that the statement meets all the rules, then it is logically correct. Exercises in developing the skill of using these rules allow you to create a culture of thinking.
General definition of syllogism and types of terms
The rules of syllogism follow from the general definition of this term. This concept is one of the forms of deductive thinking, which is characterized by the formation of a conclusion from two statements (called premises). The most common and primitive form is a simple categorical syllogism, built on 3 terms. As an illustrative example, we can cite the following conclusion:
- The first premise: "All vegetables are plants."
- Second premise: "Pumpkin is a vegetable."
- Conclusion: "Therefore, pumpkin is a plant."
The smaller term S is the subject of logical judgment, which is included in the conclusion. In the given example - “pumpkin” (subject of conclusion). Accordingly, the package containing it is called less (number 2).
The average, mediating term M is present in the premises, but is not contained in the report (“vegetable”). A parcel with a statement about it is also called average (number 1).
The larger term P, called the conclusion predicate (“plant”), is a statement made about the subject, which is a big premise (number 3). To facilitate analysis in logic, a larger term is located in the first premise.
In a general sense, a simple categorical syllogism is a subject-predicate inference that establishes the relationship between smaller and larger terms, taking into account their connection with the middle term.
The middle term may have a different arrangement in the package system. In this regard, there are 4 figures shown in the figure below.
Logical relationships showing the relationship of these terms are called modes.
The rules of syllogisms and their meaning
If the relations between the premises (modes) are built logically, a valid conclusion can be drawn from them, then they say that the syllogism is built correctly. There are special rules for identifying incorrect deductive conclusions. If at least one of them is violated, then the syllogism is wrong.
There are 3 groups of syllogism rules: rules of terms, premises and rules of figures. There are twelve in all. In determining whether the syllogism is correct, one can ignore the truth of the premises themselves, that is, their content. The main thing is to make the right conclusion from them. For the conclusion to become correct, it is necessary to correctly connect the larger and smaller terms. Therefore, they also distinguish between the form (the relationship between the terms) and the content of the syllogism. So, the statement “Tigers are herbivores. Sheep eat tigers. Therefore, rams are herbivores ”in the content of the first and second premises is false, but its conclusion is correct.
The rules of simple categorical syllogism are:
1. Rules for terms:
- "Three terms."
- "Distributions of the average term."
- "Relations of conclusion and premise."
2. For packages:
- "Three categorical judgments."
- "Lack of conclusion with two negative judgments."
- "Negative conclusion."
- "Private judgment."
- "Details of the conclusion."
For each of the logical figures, they use their own rules (there are only four of them), described below.
There are also complex syllogisms (sorites) that consist of several simple ones. In their structural chain, each conclusion serves as a premise for obtaining the following conclusion. If, starting with the second of them, the smallest premise in the expression is omitted, then such a syllogism is called Aristotelian.
Even in ancient Greece, syllogisms were considered one of the most important tools of scientific knowledge, since they help to combine concepts. The main task of the correct scientific construction of the inference is to find the middle concept, due to which syllogization is carried out. As a result of the combination of formal concepts in the mind, a person can know the real things in nature.
On the other hand, syllogism consists of concepts that generalize the properties of objects. If the concepts are not constructed correctly, as in the example of tigers and sheep, then the syllogism will not be accurate.
Approval Validation Methods
In logic, 3 practical methods of checking the correctness of syllogisms are used:
- creation of circular diagrams (image of volumes) with premises and conclusions;
- drawing up the opposite example;
- checking for consistency of syllogism with general rules and rules of figures.
The most obvious and often used way is the first.
Rule 3 Terms
This rule of categorical syllogism is as follows: there must be exactly 3 terms. The logical conclusion is built on the relationship of larger and smaller terms to the mean. If the number of terms is greater, then the establishment of complete equality among objects of different meanings, which are defined as the average term, can occur:
“The braid is a hand tool. This hairstyle is a braid. This hairstyle is a hand tool. ”
In this conclusion, the word “braid” hides two different concepts - a tool for mowing grass and a braid made from hair. Thus, there are 4 concepts, not three. The result is a distortion of meaning. This general rule of syllogisms is one of the main ones in logic.
If there are fewer terms, then it is impossible to draw any conclusions from the premises. For example: “All cats are mammals. All mammals are animals. ” Here it can be logically understood that the result of the conclusion will be the conclusion that all cats are animals. But formally, such a conclusion cannot be drawn, since only 2 concepts are present in the syllogism.
The distribution rule of the average syllogism
The meaning of the second rule of categorical syllogism is as follows: the middle of the terms must be distributed in at least one premise.
“All the butterflies fly. Some insects fly. Some insects are butterflies. ”
In this case, the term M is not distributed in the premises. To establish a relationship between extreme terms is not possible. And although the conclusion is correct in meaning, logically it is incorrect.
The rule of communication between the conclusion and the premise
The third rule of syllogism terms states that the term in the final conclusion must be distributed in the premises. In relation to the previous syllogism, it will look like this: “All the butterflies fly. Some insects are butterflies. Some insects fly. ”
Wrong option that violates the rule of simple syllogism: “All butterflies fly. No beetle is a butterfly. Not a single bug flies. ”
Parcel Rule No. 1: 3 categorical judgments
The first rule of the premises of syllogisms follows from the reformulation of the definition of the concept of simple categorical syllogism: there must be 3 categorical judgments (positive or negative), which consist of 2 premises and 1 conclusion. It echoes the first rule of terms.
Under a categorical judgment is understood a statement in which the statement or denial of any property or attribute of an object (subject) is made.
PP No. 2: the absence of a conclusion in the presence of two negative judgments
The second rule, characterizing the relationship between the premises of logical reasoning, states: from 2 premises of a negative nature it is impossible to draw a conclusion. There is also a similar reformulation: at least one of the premises in the expressions must be affirmative.
In fact, we can take such a vivid example: “An oval is not a circle. A square is not an oval. ” No logical conclusion can be drawn from it, since nothing can be obtained from the ratio of the terms “oval” and “square”. Extreme terms (larger and smaller) are excluded from the middle. Therefore, there is no definite relationship between them.
PP No. 3: the condition of the negative conclusion
Rule three: the conclusion is negative only if one of the premises is also negative. An example of the application of this rule: “Fish cannot live on land. Gudgeon is a fish. Gudgeon cannot live on land. ”
In this statement, the middle term is removed from the larger. In this regard, the extreme term (“fish”), which is part of the middle term (second statement), is excluded from the second extreme term. This rule is obvious.
PP No. 4: rule of private judgment
The fourth rule of premises is similar to the first rule of simple categorical syllogism. It consists in the following: if there are 2 private judgments in the syllogism, then a conclusion cannot be obtained. Private judgments are understood as those in which the denial or affirmation of a certain part of objects belonging to the group of objects having common features is made. Usually they are expressed in the form of statements: "Some S are not (or, conversely, are) P".
A good example that demonstrates this rule: “Some athletes set world records. Some students are athletes. ” To deduce from this the conclusion that part of “some students” sets world records is impossible. If we turn to the second rule of the terms of syllogisms, we can see that the middle term is not distributed in the premises. Therefore, such a syllogism is incorrect.
When a statement is a combination of partial affirmative and partial negative premises, then only the predicate of the partial negative statement will be distributed in the structure of the syllogism, which is also wrong.
If both premises are partial negative, then in this case the second rule of premises is triggered. Thus, at least one of the premises in the statement must have the character of a general judgment.
PP â„–5: particular conclusion
According to the fifth rule of premises of syllogisms, if at least one premise is a particular argument, then the conclusion also becomes particular.
Example: “All city artists took part in the exhibition. Some of the employees are artists. Some employees took part in the exhibition. ” This is a faithful syllogism.
An example of a private negative conclusion: “All winners received awards. Some of the present awards do not have. Some of those present are not winners. ” In this case, both the subject and the predicate of general negative judgment are distributed.
Rules of the first and second figures
The rules of categorical syllogism figures were introduced in order to clearly describe the criteria for correct judgments, which are characteristic only for this figure.
The rule of the first figure states: the smaller of the premises should be affirmative, and the larger should be general. Examples of incorrect syllogisms for this figure:
- “All humans are animals. No cat is human. No cat is an animal. ” The smaller premise is negative, so the syllogism is wrong.
- “Some plants grow in the desert. All water lilies are plants. Some water lilies grow in deserts. ” In this case, it is clear that the largest of the premises is a private judgment.
The rule that is used to describe the second figure of categorical syllogism: the largest of the premises should be general, and one of the premises should serve as a negation.
Examples of erroneous statements:
- “All crocodiles are predators. Some mammals are predators. Some mammals are crocodiles. ” Both premises are affirmative, therefore the syllogism is incorrect.
- “Some of the people may be mothers. No man can be a mother. Some men cannot be human. ” Most of the premises is a private judgment, therefore, the conclusion is erroneous.
Rules of the third and fourth figures
The third rule of syllogism figures is related to the distribution of the smaller syllogism term. If such a distribution is absent in the premise, then it cannot be distributed in the conclusion. Therefore, the following rule is required: the smaller of the premises must be affirmative, and the conclusion must be a private statement.
Example: “All lizards are reptiles. Some reptiles are not oviparous. Some egg-laying are not reptiles. " In this case, the smaller premise is not affirmative, but negative, so the syllogism is wrong.
The fourth figure is the least common, since obtaining an opinion on the basis of its premises is unnatural for the judgment process. In practice, the first figure is used to draw conclusions of this type. The rule for this figure is this: in the fourth figure, the conclusion cannot be affirmative.