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

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

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#Deduction

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