Rules of Categorical Syllogism:
1. A syllogism must contain three and only three propositions, neither more nor less.
Syllogism is always composed of three propositions, namely the major premise in which major and middle terms are compared, minor premise in which minor and middle terms are compared; and a conclusion in which the minor and the major terms are related together.
2. A syllogism must contain three and only three terms, neither more nor less.
A syllogism is the comparison to two terms, major and minor, by means of third term that is middle term. From this rule it follows that no term should be ambiguous, because if it is ambiguous it equals to two terms and then syllogism will have four terms and will not remain syllogism any more. If it has less than three terms then it is the matter of immediate inference and not syllogism.
3. The middle term must be distributed at least once in the premises.
By this we mean that the whole of middle term must be referred to in one premise at least. It serves as a link between the two extremes, the major and the minor terms. If the middle term, with which the other two terms are compared, is undistributed it means that part of it is compared with major term and part of it with minor term, hence it fails to serve as a link between the two terms and we cannot draw a conclusion. For example if we say All Punjabis are men and All Bengalis are men. The middle term ‘men’ is undistributed in both so we cannot draw a conclusion.
4. No term must be distributed in the conclusion if it is not distributed in the premise which contains it. If a major term is undistributed in major premise it cannot be distributed in conclusion, similarly if minor term is undistributed in minor premise it cannot be distributed in conclusion. We have read that in syllogism conclusion is less general than the premises which mean no term can have greater extension in the conclusion than its premise.
5. From two negative premises there can be no conclusion. A negative proposition shows that there is no connection between its terms. Now if both the premises are negative it means the middle term do not have any connection with major and minor terms. And therefore we cannot draw any conclusion from it. The relation of major and minor terms is established through middle term. If both premises are negative the middle term will have no connection with both major and minor terms. Therefore in order that a syllogism may be valid one of its premises at least must be affirmative.
6. If one premise is negative, the conclusion must be negative; and if the conclusion is negative one premise must be negative. If one premise is negative and the other is affirmative it means that middle term agrees with one extreme and disagrees with the other extreme. So the extremes will obviously disagree with each other in conclusion, which follows that conclusion will be negative. For example
Men are not perfect.
Lawyers are men. The only conclusion that can be drawn is that,
Therefore lawyers are not perfect.
7. From two particular premises there can be no conclusion. Two particular premises cannot yield any conclusion, so in every valid syllogism at least one premise must be universal.
8. If one premise is particular the conclusion must be particular. A universal conclusion can be drawn only from two universal premises and if one premise is particular the conclusion must be particular.
9. From a particular major premise and a negative minor premise there can be no conclusion. No conclusion can be followed from a combination of a particular major premise and a negative minor premise.
The Mood and Figure of Syllogism
Mood: Every Syllogism has a mood. And its mood is determined by the type of its propositions that is to say, A, E, I, O. So the mood of syllogism is represented in three letters, and these letters are always given in standard form order. By order we mean the first letter names the major premise, the second letter minor premise and the third letter names the conclusion. For example we say
No politicians are professors. (E)
Some doctors are professors. (I)
Therefore some doctors are not politicians. (O)
The mood of the above syllogism is EIO.
Figure: The mood of a standard form syllogism is not enough to characterize its logical form. Two syllogisms with the same mood can be logically different. For example mood AII can both be valid and invalid. So their form can be shown more clearly by their figure. And this is the different possible positions of middle term which constitute the figures. There can be only four figures as there can be only four positions of combination of middle term
1. The middle term may be subject term of the major premise and predicate term of the minor premise.
All M P Figure-1
All S M
2. The middle term can be the predicate term of both premises.
All P M Figure-2
All S M
3. The middle term may be the subject of both premises.
All M P Figure-3
All M S
4. The middle term may be the predicate term of major premise and subject term of the minor premise.
All P M Figure-4
All M S
So the mood and figure of this syllogism is as follows;
All Men are mortal. (A)
All Students are men. (A)
Therefore All Students are mortal. (A)
AAA-1
Here the term ‘men’ is middle term and it is the subject of the major premise and the predicate of the minor premise therefore the figure of it is 1. And as all of the three propositions are universal affirmative that is why the mood of this syllogism is AAA.
1. A syllogism must contain three and only three propositions, neither more nor less.
Syllogism is always composed of three propositions, namely the major premise in which major and middle terms are compared, minor premise in which minor and middle terms are compared; and a conclusion in which the minor and the major terms are related together.
2. A syllogism must contain three and only three terms, neither more nor less.
A syllogism is the comparison to two terms, major and minor, by means of third term that is middle term. From this rule it follows that no term should be ambiguous, because if it is ambiguous it equals to two terms and then syllogism will have four terms and will not remain syllogism any more. If it has less than three terms then it is the matter of immediate inference and not syllogism.
3. The middle term must be distributed at least once in the premises.
By this we mean that the whole of middle term must be referred to in one premise at least. It serves as a link between the two extremes, the major and the minor terms. If the middle term, with which the other two terms are compared, is undistributed it means that part of it is compared with major term and part of it with minor term, hence it fails to serve as a link between the two terms and we cannot draw a conclusion. For example if we say All Punjabis are men and All Bengalis are men. The middle term ‘men’ is undistributed in both so we cannot draw a conclusion.
4. No term must be distributed in the conclusion if it is not distributed in the premise which contains it. If a major term is undistributed in major premise it cannot be distributed in conclusion, similarly if minor term is undistributed in minor premise it cannot be distributed in conclusion. We have read that in syllogism conclusion is less general than the premises which mean no term can have greater extension in the conclusion than its premise.
5. From two negative premises there can be no conclusion. A negative proposition shows that there is no connection between its terms. Now if both the premises are negative it means the middle term do not have any connection with major and minor terms. And therefore we cannot draw any conclusion from it. The relation of major and minor terms is established through middle term. If both premises are negative the middle term will have no connection with both major and minor terms. Therefore in order that a syllogism may be valid one of its premises at least must be affirmative.
6. If one premise is negative, the conclusion must be negative; and if the conclusion is negative one premise must be negative. If one premise is negative and the other is affirmative it means that middle term agrees with one extreme and disagrees with the other extreme. So the extremes will obviously disagree with each other in conclusion, which follows that conclusion will be negative. For example
Men are not perfect.
Lawyers are men. The only conclusion that can be drawn is that,
Therefore lawyers are not perfect.
7. From two particular premises there can be no conclusion. Two particular premises cannot yield any conclusion, so in every valid syllogism at least one premise must be universal.
8. If one premise is particular the conclusion must be particular. A universal conclusion can be drawn only from two universal premises and if one premise is particular the conclusion must be particular.
9. From a particular major premise and a negative minor premise there can be no conclusion. No conclusion can be followed from a combination of a particular major premise and a negative minor premise.
The Mood and Figure of Syllogism
Mood: Every Syllogism has a mood. And its mood is determined by the type of its propositions that is to say, A, E, I, O. So the mood of syllogism is represented in three letters, and these letters are always given in standard form order. By order we mean the first letter names the major premise, the second letter minor premise and the third letter names the conclusion. For example we say
No politicians are professors. (E)
Some doctors are professors. (I)
Therefore some doctors are not politicians. (O)
The mood of the above syllogism is EIO.
Figure: The mood of a standard form syllogism is not enough to characterize its logical form. Two syllogisms with the same mood can be logically different. For example mood AII can both be valid and invalid. So their form can be shown more clearly by their figure. And this is the different possible positions of middle term which constitute the figures. There can be only four figures as there can be only four positions of combination of middle term
1. The middle term may be subject term of the major premise and predicate term of the minor premise.
All M P Figure-1
All S M
2. The middle term can be the predicate term of both premises.
All P M Figure-2
All S M
3. The middle term may be the subject of both premises.
All M P Figure-3
All M S
4. The middle term may be the predicate term of major premise and subject term of the minor premise.
All P M Figure-4
All M S
So the mood and figure of this syllogism is as follows;
All Men are mortal. (A)
All Students are men. (A)
Therefore All Students are mortal. (A)
AAA-1
Here the term ‘men’ is middle term and it is the subject of the major premise and the predicate of the minor premise therefore the figure of it is 1. And as all of the three propositions are universal affirmative that is why the mood of this syllogism is AAA.
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