1. THE CATEGORICAL
SYLLOGISM
Michael Jhon M. Tamayao, M.A. Phil.
LOGIC
College of Medical Technology
Cagayan State University

2. Topics
I.I. INTRODUCTIONINTRODUCTION
 Review of categorical
propositions
I.I. RULES FORRULES FOR
MAKING VALIDMAKING VALID
CATEGORICALCATEGORICAL
SYLLOGISMSSYLLOGISMS
 The 10 rules
III.III. THE STANDARDTHE STANDARD
FORMS OF A VALIDFORMS OF A VALID
CATEGORICALCATEGORICAL
SYLLOGISMSYLLOGISM
 Figures
 Moods
 The Valid Forms of
Categorical
Syllogisms
III.III. SUMMARYSUMMARY

3. Objectives
 At the end of the discussion, the participants
should have:
 Acquainted themselves with the rules for making
valid categorical syllogisms.
 Understood what is meant by mood, figure, &
form.
 Acquainted themselves with the valid forms of
categorical syllogisms.
 Acquired the abilities to make a valid categorical
syllogism.

4. I. INTRODUCTION
 Review of the Categorical Propositions:
TYP
E
FORM QUANTIT
Y
QUALITY DISTRIBUTION
Subject
Predicate
A All S is P Universal Affirmative Distributed Undistributed
E No S is P Universal Negative Distributed Distributed
I Some S is P Particular Affirmative Undistributed Undistributed
O Some S is not P Particular Negative Undistributed Distributed

5. 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.

6. II. RULES FOR MAKING
VALID CATEGORICAL
SYLLOGISMS
 1. A valid categorical syllogism only
has three terms: the major, the minor,
and the middle term.
MIDDLE TERM
2
Major Term
1
MinorTerm
3

7. II. RULES FOR MAKING
VALID CATEGORICAL
SYLLOGISMS
 Ex.
All politicians are sociable people.
All councilors are politicians.
Therefore, all councilors are sociable
people.
Politicians
(Middle Term)
Sociable
People
(Major Term)
Councilors
(Minor Term)

8. Sociable People
II. RULES FOR MAKING
VALID CATEGORICAL
SYLLOGISMS
Politician
s
Councilors

9. II. RULES FOR MAKING
VALID CATEGORICAL
SYLLOGISMS
 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.

10. II. RULES FOR MAKING
VALID CATEGORICAL
SYLLOGISMS
 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.

11. II. RULES FOR MAKING
VALID CATEGORICAL
SYLLOGISMS
Politicians
(Middle Term)
Sociable
People
(Major Term)
Councilors
(Minor Term)
PoliticiansPoliticians
(Middle Term)(Middle Term)
Sociable
People
(Major Term)
Councilors
(Minor Term)
Conclusion
First Premise Second Premise

12. II. RULES FOR MAKING
VALID CATEGORICAL
SYLLOGISMS
 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.
“Each & every”
X
“Each & every”
Z
“Some”
Y
“Each & every”
Z
“Some”
X
“Some”
Y

13. II. RULES FOR MAKING
VALID CATEGORICAL
SYLLOGISMS
 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.

14. “ALL” Animals
II. RULES FOR MAKING
VALID CATEGORICAL
SYLLOGISMS
Some animals are pigs.
All cats are animals.
Some cats are pigs.
Some
animals
Some
animals PigsCats
There is a possibility
that the middle term
is not the same.

15. II. RULES FOR MAKING
VALID CATEGORICAL
SYLLOGISMS
Some gamblers are cheaters.
Some Filipinos are gamblers.
Some Filipinos are cheaters.
Some
gamblers
Some
gamblers CheatersFilipinos
“ALL” Gamblers
There is a possibility
that the middle term
is not the same.

16. II. RULES FOR MAKING
VALID CATEGORICAL
SYLLOGISMS
 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)

17. II. RULES FOR MAKING
VALID CATEGORICAL
SYLLOGISMS
 Ex.
All gamblers are risk-takers. (A)
Some Filipinos are gamblers. (I)
Some Filipinos are risk-takers. (I)
All
gamblers
Risk-takers
Filipinos
Some Filipinos who
are gamblers.

18. II. RULES FOR MAKING
VALID CATEGORICAL
SYLLOGISMS
 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)
Mm
V
M
m
V

19. II. RULES FOR MAKING
VALID CATEGORICAL
SYLLOGISMS
 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)
Mm
V
M
m
V
No possible relation.

20. II. RULES FOR MAKING
VALID CATEGORICAL
SYLLOGISMS
 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)
Mm
V
M
m
V
No possible relation.

21. II. RULES FOR MAKING
VALID CATEGORICAL
SYLLOGISMS
 9. In a valid categorical syllogism, if a
premise is particular, the conclusion
must also be particular.
Ex.
All angles are winged-beings. (A)
Some creatures are angles. (I)
Some creatures are winged-beings. (I)
“Each & every”
V
“Some”
m
“Some”
M
“Some”
m
“Some”
V
“Some”
M

22. II. RULES FOR MAKING
VALID CATEGORICAL
SYLLOGISMS
 9. In a valid categorical syllogism, if a
premise is particular, the conclusion
must also be particular.
Ex.
All angles are winged-beings. (A)
Some creatures are angles. (I)
“Each & every”
V
“ALL”
m
“Some”
M
“Some”
m
“Some”
V
“Some”
M
All creatures are winged-beings. (A)

23. II. RULES FOR MAKING
VALID CATEGORICAL
SYLLOGISMS
 10. In a valid categorical syllogism, the
actual real existence of a subject may not
be asserted in the conclusion unless it
has been asserted in the premises.
 Ex.
This wood floats.
That wood floats.
Therefore, all wood floats.

24. 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.

25. III. THE STANDARD FORMS OF A
VALID CATEGORICAL
SYLLOGISM
 FIGURES:
M is P
S is M
S is P
(Figure 1)
P is M
S is M
S is P
(Figure 2)
P is M
M is S
S is P
(Figure 4)
M is P
M is S
S is P
(Figure 3)

26. III. THE STANDARD FORMS OF A
VALID CATEGORICAL
SYLLOGISM
 MOODS:
4 types of categorical propositions (A, E, I, O)
Each type can be used thrice in an argument.
There are possible four figures.
Calculation: There can be 256 possible forms of a
categorical syllogism.
 But only 16 forms are valid.

27. III. THE STANDARD FORMS OF A
VALID CATEGORICAL
SYLLOGISM
 Valid forms for the first figure:
Major Premise
A A E E
Minor Premise
A I A I
Conclusion
A I E I
 Simple tips to be observed in the first figure:
1. The major premise must be universal. (A or E)
2. The minor premise must be affirmative. (A or I)

28. III. THE STANDARD FORMS OF A
VALID CATEGORICAL
SYLLOGISM
 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:
1. The major premise must be universal. (A or E)
2. At least one premise must be negative.

29. III. THE STANDARD FORMS OF A
VALID CATEGORICAL
SYLLOGISM
 Valid forms for the third figure:
 Simple tips to be observes in the third figure:
1. The minor premise must be affirmative (A or I).
2. The conclusion must be particular (I or O).
Major Premise
A A E E I O
Minor Premise
A I A I A A
Conclusion
I I O O I O

30. III. THE STANDARD FORMS OF A
VALID CATEGORICAL
SYLLOGISM
 Valid forms for the fourth figure:
Major Premise
A A E E I
Minor Premise
A E A I A
Conclusion
I E O O I
 Three rules are to be observed:
1. If the major premise is affirmative, the major premise
must be universal.
2. If the minor premise is affirmative, the conclusion
must be particular.
3. If a premise (and the conclusion) is negative, the
major premise must be universal.

31. SUMMARY
 Summarizing all the valid forms, we have the
following table:
Figure Mood
1 AAA
1 AII
1 EAA
1 EII
Figure Mood
2 AEE
2 AOO
2 EAE
2 EIO
Figure Mood
3 AAI
3 AII
3 EAO
3 EIO
3 IAI
3 OAO
Figure Mood
4 AAI
4 AEE
4 EAO
4 EIO
4 IAI