This document discusses the categorical syllogism, which is a deductive argument composed of three categorical propositions using only three distinct terms. It provides examples and outlines 8 rules for making valid categorical syllogisms, including that they must have only 3 terms, each term must occur in two propositions, and the conclusion's terms must be distributed as in the premises. It also describes the 4 figures of categorical syllogisms based on the arrangement of terms, and the valid moods for each figure defined by the propositions' quantity and quality.

1. THE CATEGORICAL SYLLOGISM
(Michael Jhon Tamayao, M.A. Phil.)
I. INTRODUCTION
What is a categorical syllogism?
It is kind of a mediate deductive argument, which is composed of three standard form
categorical propositions that uses only three distinct terms.
Ex.
All politicians are good in rhetoric.
All councilors are politicians.
Therefore, all councilors are good in rhetoric.
II. RULES FOR MAKING VALID CATEGORICAL SYLLOGISMS
1. A valid categorical syllogism only has three terms: the major, the minor, and the
middle term.
Ex.
All politicians are sociable people.
All councilors are politicians.
Therefore, all councilors are sociable people.
The major term is predicate of the conclusion. It appears in the Major Premise (which is usually
the first premise).
The minor term is the subject of the conclusion. It appears in the Minor Premise (which is
usually the second premise).
The middle term is the term that connects or separates other terms completely or partially.
2. Each term of a valid categorical syllogism must occur in two propositions of the
argument.
Ex.
All politicians are sociable people.
All councilors are politicians.
Therefore, all councilors are sociable people.
Politicians – occurs in the first and second premise.
Sociable People – occurs in the first premise and conclusion.
Councilors – occurs in the second premise and conclusion.
3. In a valid categorical syllogism, a major or minor term may not be universal (or
distributed) in the conclusion unless they are universal (or distributed) in the premises.

2. 4. The middle term in a valid categorical syllogism must be distributed in at least one of
its occurrence.
Ex.
Some animals are pigs.
All cats are animals.
Some cats are pigs
5. In a valid categorical syllogism, if both premises are affirmative, then the conclusion
must be affirmative.
Ex.
All risk-takers are gamblers. (A)
Some Filipinos are gamblers . (I)
Some Filipinos are risk-takers. (I)
6. In a valid categorical syllogism, if one premise is affirmative and the other negative,
the conclusion must be negative
Ex.
No computer is useless. (E)
All ATM are computers. (A)
No ATM is useless. (E)
7. No valid categorical proposition can have two negative premises.
Ex.
No country is leaderless. (E)
No ocean is a country. (E)
No ocean is leaderless. (E)

3. 8. At least one premise must be universal in a valid categorical syllogism.
Ex.
Some kids are music-lovers. (I)
Some Filipinos are kids. (I)
Some Filipinos are music-lovers. (I)
9. In a valid categorical syllogism, if a premise is particular, the conclusion must also be
particular.
Ex.
All angels are winged-beings. (A)
Some creatures are angels. (I)
Some creatures are winged-beings. (I)
III. THE STANDARD FORMS OF A VALID CATEGORICAL SYLLOGISM
The logical form is the structure of the categorical syllogism as indicated by its “figure” and
“mood.”
“Figure” is the arrangement of the terms (major, minor, and middle) of the argument.
“Mood” is the arrangement of the propositions by quantity and quality.

4. FIGURES:
where: M---is the middle term
P---is the major term
S—is the minor term
Figure 1. The middle term is a subject of the first statement(major premise)and
predicate of the second statement(minor premise)----subpre
Figure 2. The middle term is a predicate of the first statement(major premise)and the
second statement(minor premise)-----prepre
Figure 3. The middle term is the subject of the first statement(major premise)and the
second statement(minor premise)-----subsub
Figure 4. The middle term is a predicate of the first statement(major premise)and the
subject of the second statement(minor premise)-----presub
M is P
S is M
S is P
(Figure 1)
P is M
S is M
S is P
(Figure 2)
M is P
M is S
S is P
(Figure 3)
P is M
M is S
S is P
(Figure 4)

5. MOODS:
4 types of categorical propositions (A, E, I, O)
Each type can be used thrice in an argument.
There are possible four figures.
Valid forms for the first figure:
Major Premise A A E E
Minor Premise A I A I
Conclusion A I E 0
Simple tips to be observed in the first figure:
The major premise must be universal. (A or E)
The minor premise must be affirmative. (A or I)

6. Valid forms for the second figure:
Major Premise A A E E
Minor Premise E O A I
Conclusion E O E O
Simple tips to be observed in the second figure:
The major premise must be universal. (A or E)
At least one premise must be negative.

7. Valid forms for the third figure:
Major Premise A A E E I
Minor Premise A I A I A
Conclusion I I O O I
Simple tips to be observes in the third figure:
The minor premise must be affirmative (A or I).
The conclusion must be particular (I or O).

8. Valid forms for the fourth figure:
Major Premise A A E E
Minor Premise A E A I
Conclusion I E O O
Three rules are to be observed:
If the major premise is affirmative, the major premise must be universal.
If the minor premise is affirmative, the conclusion must be particular.
If a premise (and the conclusion) is negative, the major premise must be universal.