Maharashtra Board Class 12 Logic Chapter 5 Syllogism PDF Download

Syllogism

In the previous chapter we have studied the meaning of Mediate inference. We already know that Syllogism is an mediate inference. In this chapter we will deal with Categorical Syllogism.

Categorical Syllogism in general is a deductive argument, in which the conclusion cannot assert more than what is asserted in the premises.

Let us have two categorical propositions as premises.

Some Indians are Honest.

No Indians are fools.

Which conclusion given below is the correct one, that follows from the above two premises?

1. Some Indians are fools.

2. Some honest persons are not fools.

Categorical Syllogism

The theory of Categorical Syllogism was put forward by Aristotle.

Categorical syllogism is defined as a deductive argument consisting of three categorical propositions that together contain exactly three terms, each of which occurs in only two of the constituent propositions.

According to Aristotle, Categorical Syllogism is an argument in which the middle term stands in a certain relation to the other two terms. i.e. the Subject term and the Predicate term.

It is a mediate inference in which the conclusion is deduced from two given propositions.

For example:

All fruits are ripe.

All apples are fruits.

Therefore all apples are ripe.

In the above syllogism the first two propositions are the premises and the third proposition is the conclusion.

As a mediate inference, syllogism differs from immediate inference. Unlike eductions and opposition of propositions, the conclusion of syllogism is deduced from the two premises taken jointly. It is not deducted from each of the premises, separately.

Teacher's Note

Syllogism is a way to check if our thinking is correct. Like checking if your answer in maths is right by using the rules.

Exam Trick

Remember: Syllogism has THREE things - two premises and one conclusion. Just like a story has a beginning, middle and end.

Points to Remember

Syllogism is a type of mediate inference.
It has three propositions - two premises and one conclusion.
The conclusion comes from both premises together, not just one.
Syllogism is about checking if logic is correct.

Structure Of Categorical Syllogism

In a Categorical syllogism, the constituent propositions are analysed into terms. The predicate term of the conclusion is called the major term. It is represented by 'P' and the Subject term of the conclusion is called the minor term. It is represented by 'S'. The term which occurs in both the premises, but not in the conclusion is called the middle term. It is represented by 'M'.

The premise in which the major term occurs is called major premise and the premise in which the minor term occurs is called minor premise. Middle term relates the major and minor terms. The relation between the middle term and the other two terms is either of affirmation or negation.

Categorical Syllogism is a formal inference. Its validity does not depend on the content of, either the premise or the conclusion. Hence syllogistic argument can be represented symbolically, and its validity is decided on the basis of formal relation between the premises and the conclusion. If the premises imply the conclusion, the inference is valid and if they do not imply the conclusion, the inference is invalid.

Teacher's Note

Think of P, S, and M like three friends. P is the biggest idea, S is the smallest idea, and M is the middle friend who knows both of them.

Exam Trick

Remember: Major term = Predicate (P). Minor term = Subject (S). Middle term = Middle (M). P, S, M - easy!

Points to Remember

Major term is the predicate of the conclusion (P).
Minor term is the subject of the conclusion (S).
Middle term is in both premises but not in conclusion (M).
Major premise has the major term (P).
Minor premise has the minor term (S).

Figures Of Categorical Syllogism

Categorical Syllogisms differ from each other depending upon the position of the middle term in the premises. The middle term may stand as the subject or the predicate in the premises. There are three kinds of syllogism depending on the position of middle term in the premises. They are called figures. Galen has added the fourth figure to the syllogism. Thus there are four figures of syllogism. Figures of syllogism is the form of syllogism as determined by the position of the middle term in the premises.

The figures of Categorical syllogism are as follows:

Figure - I: It is the form of Categorical syllogism in which the middle term stands as the subject of major premise and predicate of minor premise.

M P

S M

∴ S P

Figure - II: It is the form of Categorical syllogism in which the middle term stands as the predicate in both the premises i.e. major and minor premise.

P M

S M

∴ S P

Figure - III: It is the form of Categorical syllogism in which the middle term stands as the subject in both the premises, i.e. major and minor premise.

M P

M S

∴ S P

Figure - IV: It is the form of Categorical syllogism in which the middle term stands as the predicate in the major premise and as a subject in minor premise.

P M

M S

∴ S P

Teacher's Note

The four figures are like four different ways to arrange a family photo. The middle person (M) can stand in different positions - left, right, or middle.

Exam Trick

Remember the four figures by where M stands: Figure 1 = M first then M second. Figure 2 = M second both times. Figure 3 = M first both times. Figure 4 = M second then M first.

Points to Remember

There are four figures of syllogism based on M's position.
Figure 1 has M as subject in major and predicate in minor.
Figure 2 has M as predicate in both premises.
Figure 3 has M as subject in both premises.
Figure 4 has M as predicate in major and subject in minor.

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