# Logic-Formal and Symbolic Syllogistic Rules and Questions: 4 Terms, Middle Terms, Negative Premises

Doorsteptutor material for GATE is prepared by world's top subject experts: Get detailed illustrated notes covering entire syllabus: point-by-point for high retention.

Logic-Formal and Symbolic: Syllogistic Rules (Philosophy)

- A syllogism must establish its conclusion via performing various rules.
- To help avoid errors, or mistakes, a total number of six syllogistic rules have been set up.
- In case, if one of the rules is violated, then the syllogism commits a mistake or an error which result in it being invalid.
- In other words, for a syllogism to be logically valid, the six syllogistic rules must be followed strictly.
- The rules are;
**Rule 1**: Avoid four terms in a categorical syllogism**Rule 2**: Distribute the middle term in at least one of the premises.**Rule 3**: Avoid two negative premises

## 1. Avoid Four Terms

- A valid syllogism must contain three terms,
- Major term
- Middle term
- Minor term
- Each of these terms should be used in the same sense throughout, else it will result into an invalid syllogism.
- This means, an argument must have only three terms. The three terms are; major term, middle term and minor term.
- Each of these terms should be used in the same sense throughout the syllogism (premises and conclusion) .

For example;

- All men are mortal
- Socrates is a man
- Therefore, Socrates is mortal

For example;

- All men are mortal
- Socrates is a man
- Therefore, Socrates is mortal

Here, the major term is mortal, the middle term is men/man and the minor term is Socrates.

On the other hand, a syllogism such as;

- All men are handsome
- All Women are beautiful
- Therefore, all women are handsome

Here, more than three terms are used, such as men, handsome, women and beautiful. So, the syllogism is invalid.

## 2. Distribute Middle Term in at Least One of the Premises

- If the middle term of the syllogism in not distributed in either of the two premises, then the syllogism is termed
**invalid**. - For a valid syllogism, the middle term must be distributed in at least one of the two premises.
- It could either be the major premise or the minor premise.
- It is also important to note that the middle term
**never**appears in the conclusion in a valid syllogism.

For example, in the below syllogism

- All mammals have hair
- All whales are mammals
- Therefore, all whales have hair:
**Valid syllogism**

Here, the major term is hair, the middle term is mammals and the minor term is whales.

So, the middle term- mammals are distributed in the major premise- All mammals have hair.

Whereas, In the example given below;

- All Whales have hair
- All Animals have hair
- Therefore, all Animals are Whales

Here, the major term is whales, the middle term is hair, and the minor term is animals.

So, in an A proposition; only the subject term is distributed.

In the example given above,

- All Whales have hair- major premise - whales (subject term) distributed
- All Animals have hair - minor premise - animals (subject term) distributed

So, the middle term hair is neither distributed in the major premise nor the minor premise.

Therefore, the syllogism is **invalid**.

## 3. Avoid Two Negative Premises

- When a conclusion is drawn from two negative premises, the syllogism becomes
**invalid**. - In a Deductive argument, two negative premises cannot result in a conclusion
- So, the two premises cannot be E propositions, E and O propositions and both O propositions.

For example,

- No fish are mammals - E proposition: Universal and Negative
- Some dogs are not fish - O proposition: Particular and Negative
- Therefore, some dogs are not mammals - O proposition
- Here, the conclusion is not possible, the syllogism is invalid.
- Where both the premises are negative, the relationship between the Subject and Predicate is denied.

## Questions

1. If the middle term of the syllogism in not distributed in either of the two premises, then the syllogism is termed ________

A. Valid

B. Invalid

C. can՚t say

D. True

Answer: B

2. For a valid syllogism, the middle term must be distributed in ________

A. One of the two premises.

B. In both the premises

C. In the major premise

D. In the minor premise

Answer: A

3. All mammals have hair; all whales are mammals. Therefore, all whales have hair.

In the above syllogism, the major term is ________

A. Hair

B. Whales

C. Mammals

D. All

Answer: A

#Syllogistic

#Rules

#Deduction

#Syllogism

#Logic

-Manishika