# Categorical Syllogism: Western Logic: Contains Categorical Propositions

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## Categorical Syllogism

- Contains Categorical Propositions
- Categorical Propositions are Standard form propositions
- They affirm or deny the inclusion or exclusion of categories or classes.

The four kinds of sentences Logic deals with have S and P which stand for the subject class and the predicate class, respectively.

- A: All S are P (universal affirmation)
- E: No S are P (universal negation)
- I: Some S are P (particular affirmation)
- O: Some S are not P (particular negation)

A categorical syllogism has exactly three propositions.

- Major Premise
- Minor Premise
- Conclusion

For example,

- All Men are Mortal
- Socrates is a Man

Therefore, Socrates is Mortal

So, it is a part of Deductive, mediate inference.

It consists of 3 propositions, the first two are premises and the third is the conclusion.

- All Men are Mortal
- Socrates is a Man

Therefore, Socrates is Mortal

- The three propositions deal with three terms: major term, middle term and minor term.
- The three terms are exactly used twice in the three propositions, in the same way.

Categorical Propositions can exist in 4 possible ways.

Also called the 4 figures of logic.

- Figure means arrangement of terms in the premises.
- Each figure is identified by the position of the middle term in the syllogism

For example:

1^{st} Figure- the middle term is the subject of the major premise and the predicate of the minor premise.

- Major premise: A A E E
- Minor premise: A I A I
- Conclusion: A i.e. O

So, the two rules of 1^{st} figure are.

1. The major premise must be universal

2. The minor premise must be affirmative

For example:

- All men are educated
- All rich are men

Therefore, all rich are educated.

- M-P
- S-M

Therefore, S-P

2^{nd} figure- the middle term is the predicate of both the premises.

- Major premise- A A E E
- Minor premise- E O A I
- Conclusion- E O E O

Rules:

1. The major premise must be universal.

2. One premise must be negative.

For example:

- No teachers are singers
- All dancers are singers

Therefore, no dancers are teachers.

- P-M
- S-M

Therefore, S-P

3^{rd} figure: middle term is the subject term of both the premises

Major premise: A A E E I O

Minor premise: A I A I A A

Conclusion: I I O O I O

Rules:

1. The minor premise must be affirmative.

2. The conclusion must be a particular

For example:

- All potassium floats on water
- All potassium is a metal

Therefore, some metal floats on water.

- M-P
- M-S

Therefore, S-P

4^{th} figure: middle term is predicate in the major premise and subject in the minor premise.

- Major premise: A A E E I
- Minor premise: A E A I A
- Conclusion: i.e. O O I

Rules:

1. If major premise is affirmative, the minor premise will be universal.

2. If minor premise is affirmative, the conclusion will be particular

3. If a premise (and the conclusion) is negative, the major premise must be universal.

For example:

- All pugs are dogs
- All dogs are animals

Therefore, some animals are pugs.

- P-M
- M-S

Therefore, S-P

## MCQs

1. P-M, M-S, therefore S-P is

A. 1^{st} figure

B. 2^{nd} figure

C. 4^{th} figure

D. None of these

Answer: C

Explanation:

M-P P-M M-P P-M

S-M S-M M-S M-S

Therefore, S-P Therefore, S-P Therefore, S-P Therefore, S-P

2. All men are walking, All Peter are men, therefore, all Peter are walking is a ________

A. 1^{st} figure

B. 2^{nd} figure

C. 4^{th} figure

D. None of these

Answer: A

Explanation: 1^{st} Figure- the middle term is the subject of the major premise and the predicate of the minor premise.

3. The major premise must be universal, and One premise must be negative are the rules of

A. 1^{st} figure

B. 2^{nd} figure

C. 4^{th} figure

D. None of these

Answer: B

Explanation: 2^{nd} figure- the middle term is the predicate of both the premises

Rules:

1. The major premise must be universal.

2. One premise must be negative.

For example:

- No teachers are singers
- All dancers are singers

Therefore, no dancers are teachers.

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-Manishika