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

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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

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

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