The general rules of syllogism and logical figures help to easily distinguish correct conclusions from incorrect ones. If in the process of mental analysis it turns out that the statement corresponds to all the rules, then it is logically correct. Exercises in developing the skill of using these rules allow you to form 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, the following conclusion can be given:
- First premise: "All vegetables are plants."
- Second premise: "Pumpkin is a vegetable."
- Conclusion: “Therefore, the pumpkin isplant.”
The lesser term S is the subject of the logical judgment included in the conclusion. In the given example - "pumpkin" (the subject of the conclusion). Accordingly, the package containing it is called the smaller one (number 2).
The middle, mediating term M is present in the premises, but not in the conclusion ("vegetable"). A premise with a statement about him is also called the middle one (number 1).
The major term P, called the predicate of the conclusion ("plant"), is a statement made about the subject, which is the major premise (number 3). To facilitate analysis in logic, the larger term is placed in the first premise.
In a general sense, a simple categorical syllogism is a subject-predicate inference that establishes a relationship between a minor and a major term, taking into account their connection with the middle term.
The middle term can have different positions in the parcel system. In this regard, 4 figures are distinguished, shown in the figure below.
Logical relations showing the relationship of these terms are called modes.
Rules of syllogisms and their meaning
If the relations between the premises (modes) are built logically, a reasonable 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 incorrect.
There are 3 groups of syllogism rules: rules of terms, premises and rules of figures. All of themthere are twelve. When determining whether a syllogism is correct, one can ignore the truth of the premises themselves, that is, their content. The main thing is to draw the right conclusion from them. In order for the conclusion to become correct, it is necessary to correctly connect the larger and smaller terms. Therefore, the form (relationship between terms) and the content of the syllogism are also distinguished. So, the statement “Tigers are herbivores. Sheep are tigers. Therefore, rams are herbivores in the content of the first and second premises is false, but his conclusion is correct.
The rules of a simple categorical syllogism are:
1. Rules for terms:
- "Three Terms".
- "Distributions of the middle term".
- "Connections of conclusion and premise".
2. For parcels:
- "Three categorical judgments".
- "Absence of a conclusion with two negative judgments."
- "A negative conclusion".
- "Private Judgments".
- "Particulars 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), which consist of several simple ones. In their structural chain, each conclusion serves as a premise for obtaining the next conclusion. If, starting from the second of them, the minor 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, as they help to connect concepts. The main task of the faithfulthe scientific construction of the conclusion is to find the middle concept, thanks to which the syllogization is carried out. As a result of the combination of formal concepts in the mind, a person can know real things in nature.
On the other hand, the syllogism consists of concepts that generalize the properties of objects. If the concepts are constructed incorrectly, as in the example of tigers and rams, then the syllogism will not be accurate.
Methods for checking assertions
In logic, there are 3 practical methods for checking the correctness of syllogisms:
- creation of circular diagrams (image of volumes) with premises and conclusions;
- composing a counterexample;
- checking for consistency of the syllogism with the general rules and rules of figures.
The most obvious and frequently used way is the first one.
Rule of 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 the larger and smaller terms to the average. If the number of terms is greater, then complete equality may occur among the properties of objects of different meanings, which are defined as the middle term:
The scythe 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 mowingherbs and a braid woven 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 inference will be the conclusion that all cats are animals. But formally, such a conclusion cannot be made, since there are only 2 concepts in the syllogism.
Distribution rule for the mean syllogism
The meaning of the second rule of the categorical syllogism is as follows: the middle of the terms must be distributed in at least one premise.
“All butterflies fly. Some insects fly. Some insects are butterflies.”
In this case, the term M is not distributed in the premises. It is not possible to establish a relationship between the extreme terms. While the conclusion is semantically correct, it is logically incorrect.
The rule for linking conclusion and premise
The third rule of the terms of the syllogism says that the term in the final conclusion must be distributed in the premises. In relation to the previous syllogism, it would look like this: “All butterflies fly. Some insects are butterflies. Some insects fly.”
Wrong option, violating the rule of simple syllogism: “All butterflies fly. No beetle is a butterfly. No beetle flies.”
The Parcel Rule (RP) 1: 3categorical judgments
The first rule of premises of syllogisms follows from the reformulation of the definition of the concept of a 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.
A categorical judgment is understood as a statement in which an assertion or denial of any property or attribute of an object (subject) is made.
PP 2: no conclusion with two negatives
The second rule characterizing the connections between the premises of logical reasoning says: it is impossible to draw a conclusion from 2 premises of a negative nature. There is also a similar reformulation: at least one of the premises in the expressions must be affirmative.
In fact, we can take this illustrative 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 relationship between the terms "oval" and "square". The extreme terms (greater and smaller) are excluded from the middle. Therefore, there is no definite relationship between them.
PP 3: negative conclusion condition
Third rule: 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. Minnow is a fish. The minnow cannot live on land.”
In this statement, the middle termremoved from the larger one. In this regard, the extreme term ("fish"), which is part of the middle one (the second statement) is excluded from the second extreme term. This rule is obvious.
PP 4: The Rule of Private Judgment
The fourth rule of premises is similar to the first rule of a simple categorical syllogism. It consists in the following: if there are 2 private judgments in the syllogism, then the conclusion cannot be obtained. Private judgments are understood as those in which a certain part of objects belonging to a group of objects with common features is denied or affirmed. Usually they are expressed as statements: "Some S are not (or, on the contrary, are) P".
An illustrative example of this rule: “Some athletes set world records. Some students are athletes." It is impossible to conclude from this that some "some students" set world records. If we turn to the second rule of syllogism terms, we can see that the middle term is not distributed in premises. Therefore, such a syllogism is incorrect.
When a statement is a combination of a particular affirmative and a particular negative premise, then only the predicate of the particular negative statement will be distributed in the structure of the syllogism, which is also wrong.
If both premises are privately 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 5:particularity of conclusion
According to the fifth rule of premises of syllogisms, if at least one premise is a particular reasoning, then the conclusion also becomes particular.
Example: “All the artists of the city took part in the exhibition. Some of the employees of the enterprise are artists. Some employees of the enterprise took part in the exhibition. This is a valid 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 the general negative judgment are distributed.
Rules of the first and second figures
The rules of categorical syllogism figures were introduced in order to visually describe the criteria for the correctness of judgments that are characteristic only for this figure.
The rule of the first figure says: the smallest of the premises must be affirmative, and the largest must be general. Examples of incorrect syllogisms for this figure:
- “All people are animals. No cat is human. No cat is an animal." The minor 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 a categorical syllogism: the largest of the premises should be general, and one of the premises should be a negation.
Examples of false statements:
- "All crocodiles are predators. Some mammals are predators. Some mammals are crocodiles." Both premises are affirmative, so the syllogism is invalid.
- "Some of the people can be mothers. No man can be a mother. Some men can't be human." Most of the premises is a private judgment, so the conclusion is erroneous.
Rules of the third and fourth pieces
The third rule of syllogism figures is related to the distribution of the minor term of the syllogism. If such a distribution is absent in the premise, then it cannot be distributed in the conclusion either. Therefore, the following rule is required: the smallest of the premises must be affirmative, and the conclusion must be a particular statement.
Example: “All lizards are reptiles. Some reptiles are not oviparous. Some oviparous are not reptiles. In this case, the minor of the premises is not affirmative, but negative, so the syllogism is incorrect.
The fourth figure is the least common, since obtaining a conclusion based on its premises is unnatural for the judgment process. In practice, the first figure is used to construct an inference of this type. The rule for this figure is as follows: in the fourth figure, the conclusion cannot be generally affirmative.
