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

2. Topics INTRODUCTION Review of categorical propositions
RULES FOR MAKING VALID CATEGORICAL SYLLOGISMS
The 10 rules
THE STANDARD FORMS OF A VALID CATEGORICAL SYLLOGISM
Figures
Moods
The Valid Forms of Categorical Syllogisms
SUMMARY

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: A All S is P
TYPE
FORM
QUANTITY
QUALITY
DISTRIBUTION
Subject Predicate A
All S is P
Universal
Affirmative
Distributed Undistributed E
No S is P
Negative
Distributed Distributed I
Some S is P
Particular
Undistributed Undistributed O
Some S is not P
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.
Sociable
People
(Major Term)
Politicians
(Middle Term)
Councilors
(Minor Term)

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

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
“Some” Y
“Each & every” Z
“Some” X
“Each & every” Z
“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. II. RULES FOR MAKING VALID CATEGORICAL SYLLOGISMS
Some animals are pigs.
All cats are animals.
Some cats are pigs.
There is a possibility
that the middle term is not the same.
“ALL” Animals
Cats
Pigs
Some
animals
Some
animals

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

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)
Risk-takers
Some Filipinos who are gamblers.
All
gamblers
Filipinos

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) 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) 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) 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 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
“Some” M
“Some” m
“Some” V
All creatures are winged-beings. (A)
“ALL” m
“Some” M

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)
M is P
M is S
S is P
(Figure 3)
P is M
M is S
S is P
(Figure 4)

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 E
Minor Premise I
Conclusion
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)

28. III. THE STANDARD FORMS OF A VALID CATEGORICAL SYLLOGISM
Valid forms for the second figure:
Major Premise A E
Minor Premise O I
Conclusion
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.

29. III. THE STANDARD FORMS OF A VALID CATEGORICAL SYLLOGISM
Valid forms for the third figure:
Major Premise A E I O
Minor Premise
Conclusion
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).

30. III. THE STANDARD FORMS OF A VALID CATEGORICAL SYLLOGISM
Valid forms for the fourth figure:
Major Premise A E I
Minor Premise
Conclusion 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.

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