Rules of Syllogism

1. Rules of Syllogism – There are five rules that govern the categorical syllogism:

Rule 1: There must be three terms and only three – the major term, the minor term, and the middle term. If there are only two terms the relationship between these two cannot be established. And if there were more than three terms this would violate the structure of the categorical syllogism.

Animals are living beings.

Plants are heavenly bodies.

Therefore…

Stones are minerals.

Minerals are stones.

Therefore…

A widower is a man.

A man is either male or female.

Therefore, a widower is either male or female.

Rule 2: Each term must occur twice in the syllogism: the major must occur in the conclusion and in one premise, the minor in the conclusion and in one premise; the middle in both premise but not in the conclusion. There must therefore be a total of three propositions in the syllogism.

Rule 3: The middle term must be distributed at least once. If the middle term is particular in both premises it might stand for a different portion of its extension in each occurrence and thus be equivalent to two terms.

All sharks are fish.

All salmon are fish.

Therefore, all salmons are sharks.

Many rich men oppress the poor.

Jones is a rich man.

Therefore, Jones oppresses the poor.

Rule 4: The major and minor terms may not be universal in the conclusion unless they are universal in the premises. If a term is distributed in the conclusion then it must be distributed first in the premise.

There is an illicit major term if the major term is universal in the conclusion but particular in the premise:

All horses are animals.

All dogs are not horses.

Therefore, all dogs are not animals.

There is an illicit minor term if the minor term is universal in the conclusion but particular in the premise:

All tigers are mammals.

All mammals are animals.

Therefore, all animals are tigers.

The rationale behind this rule is that we may not conclude about all the inferiors of a term if the premises have given us information about only some of them. The key to detect a violation of this rule is to examine the conclusion. If there is no term that is distributed in the conclusion then this rule could not have been violated. If one or both terms in the conclusion are distributed there is possibility of the rule having been violated. If a term is distributed both in the premise and the conclusion there is no violation of this rule.

Rule 5: If both premises are affirmative, the conclusion must be affirmative. The reason for this rule is that affirmative premises either unite the minor or major terms, or else do not bring them into relationship with each other at all.

All sins are detestable.

All pretenses are a sin.

Therefore, all pretenses are not detestable.

There is a need to be cautious about apparently affirmative or negative propositions:

Animals differ from angels.

Man is an animal.

Therefore, a man is not a horse.

Rule 6: If one premise is affirmative and the other negative, the conclusion must be negative.

All crows are birds.

All wolves are not crows.

Therefore, all wolves are birds.

Some premises are apparently affirmatives but actually negative and therefore yield a valid conclusion:

Dogs are not cats.

Greyhounds are dogs.

Therefore, greyhounds differ from cats.

Rule 7: If both premises are negative – and not equivalently affirmative – there can be no conclusion.

Reptiles are not mammals.

Dogs are not reptiles.

Therefore…

Rule 8: If both premises are particular there can be no conclusion.