categorical syllogism

The Categorical Syllogism and Its Rules


Is the logical process in which, the premises relate two terms with a third (middle), and the relationship is expressed in the conclusion that either unites or separates the first two terms.


Major Term
Predicate of the Conclusion, found in the Major Premise (P)

Minor Term
Subject of the Conclusion, found in the Minor Premise (S)

Middle Term
Term found in both premises (m)

Major Premise (MP)
minor premise (mp)
Conclusion (C)

+ = affirmative proposition
- = negative proposition
u = universal
p = particular
s = singular

1. If the proposition is affirmative, then the quantity of the predicate is particular.
2. If the proposition is negative, then the quantity of the predicate is universal.

Rules of the Categorical Syllogism

1. The middle term must always be taken in the same sense.

A father is a male parent;
but, the Holy Pope is a father;
therefore, the Holy Pope is a male parent.

A tablet is a compressed solid material for writing;
but, Biogesic is a tablet;
therefore, biogesic is a compressed solid material for writing.

Fallacy of Equivocation

2. The major term and the minor term cannot have a greater extension in the conclusion than in the premise.

All hammers are tools;
But, no chisels are hammers;
Ergo, no chisels are tools.

All birds have wings;
But, all birds are animals;
Ergo, all animals have wings.

Fallacy of Illicit Minor Term
Fallacy of Illicit Major Term

3. The middle term should not occur in the conclusion.

A decagon is a polygon;
but, a decagon is ten-sided;
ergo, a decagon is a ten-sided polygon.

Fallacy of Misplaced Middle Term

4. The middle term must be distributed universally, at least once, in the premises.

All horses are fast-runners;
But, all rabbits are fast-runners;
Ergo, all rabbits are horses.

All mothers are females;
But, some females are barren
Ergo, some barren persons are mothers.

Fallacy of Undistributed Middle Term

5. Two affirmative premises cannot give a negative conclusion.

All writers have a rich imagination;
But, Dr. Rizal is a writer;
Ergo, Dr. Rizal does not have a rich imagination.

Fallacy of A Negative Conclusion drawn from Affirmative Premises

6. From two negative premises, nothing follows.

A chair is not a table;
but, a table is not a pen;
Ergo, a pen is not a chair.

Fallacy of Negative Premises

7. From two particular premises, nothing follows.

Some men are old;
Some old people are women
Some women are men.

Some cows are animals;
Some dogs are not cows
Some dogs are not animals.

Some delegates are not foreigners
Some Americans are delegates
Some Americans are not foreigners.

Fallacy of Particular Premises

8. The conclusion follows the weaker premise.

All roses are flowers
Some roses are fragrant
All fragrant things are flowers

All rebels are deviants
Some students are not deviants
Some students are rebels

Fallacy of Universal Conclusion drawn from a Particular Premise
Fallacy of Affirmative Conclusion drawn from a Negative Premise