THE CATEGORICAL SYLLOGISM

ARBIND KUMAR SINGH

Logical ReasoningAlternative Learning System

NEW DELHI

TopicsI.I. INTRODUCTIONINTRODUCTION

Review of categorical propositions

II.II. RULES FOR RULES FOR MAKING VALID MAKING VALID CATEGORICAL CATEGORICAL SYLLOGISMSSYLLOGISMS

The 10 rules

III.III. THE STANDARD THE STANDARD FORMS OF A VALID FORMS OF A VALID CATEGORICAL CATEGORICAL SYLLOGISMSYLLOGISM

Figures Moods The Valid Forms of

Categorical Syllogisms

IV.IV. SUMMARYSUMMARY

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.

I. INTRODUCTION Review of the Categorical

Propositions:TYPE

FORM QUANTITY

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

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.

MIDDLE TERM2

Major Term1

MinorTerm3

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)

Sociable People

II. RULES FOR MAKING VALID CATEGORICAL SYLLOGISMS

Politicians

Councilors

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.

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.

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

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

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.

“ALL” Animals

II. RULES FOR MAKING VALID CATEGORICAL SYLLOGISMS

Some animals are pigs.

All cats are animals.Some cats are pigs.

Someanimals

Someanimals PigsCats

There is a possibility

that the middle term is not the same.

II. RULES FOR MAKING VALID CATEGORICAL SYLLOGISMS

Some gamblers are cheaters.

Some Filipinos are gamblers.

Some Filipinos are cheaters.

Somegamblers

Somegamblers CheatersFilipinos

“ALL” Gamblers

There is a possibility

that the middle term is not the same.

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)

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)

Allgamblers

Risk-takers

Filipinos

Some Filipinos who are gamblers.

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

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.

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.

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

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)

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.

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.

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)

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.

III. THE STANDARD FORMS OF A VALID CATEGORICAL SYLLOGISM

Valid forms for the first figure:

Major Premise A A E EMinor Premise A I A IConclusion 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)

III. THE STANDARD FORMS OF A VALID CATEGORICAL SYLLOGISM

Valid forms for the second figure:

Major Premise A A E EMinor Premise E O A IConclusion 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.

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

III. THE STANDARD FORMS OF A VALID CATEGORICAL SYLLOGISM

Valid forms for the fourth figure:

Major Premise

A A E E IMinor Premise

A E A I AConclusion 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.

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