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```					THE CATEGORICAL
SYLLOGISM
ARBIND KUMAR SINGH

Logical Reasoning
Alternative Learning System
NEW DELHI
Topics
I.        INTRODUCTION              III.       THE STANDARD
     Review of categorical              FORMS OF A VALID
propositions                       CATEGORICAL
SYLLOGISM
     Figures
     Moods
II.       RULES FOR MAKING
     The Valid Forms of
VALID CATEGORICAL
Categorical Syllogisms
SYLLOGISMS
IV.        SUMMARY
     The 10 rules
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.

Major Term        MIDDLE TERM      MinorTerm
1                  2               3
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             Politicians          Councilors
(Middle Term)        (Minor Term)
(Major Term)
II. RULES FOR MAKING VALID
CATEGORICAL SYLLOGISMS

Sociable People

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
Sociable                       Politicians
People        First Premise                   Second PremiseCouncilors
(Middle Term)               (Minor Term)
(Major Term)

Sociable                   Politicians
People                     Conclusion                 Councilors
(Middle Term)              (Minor Term)
(Major Term)
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”        “Some”
X                 Y
“Each & every”        “Some”
Z                 X

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

“ALL” Animals

Cats           Some    Some
animals animals             Pigs
II. RULES FOR MAKING VALID
CATEGORICAL SYLLOGISMS
Some gamblers are cheaters.
There is a possibility
Some Filipinos are gamblers.           that the middle term
Some Filipinos are cheaters.             is not the same.

“ALL” Gamblers

Filipinos         Some       Some
gamblers   gamblers          Cheaters
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)

Risk-takers                Some Filipinos who
are gamblers.
All
gamblers Filipinos
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.
V       M
No computer is useless.   (E)
All ATM are computers.    (A)    m       V
No ATM is useless.         (E)
m       M
II. RULES FOR MAKING VALID
CATEGORICAL SYLLOGISMS
   7. No valid categorical proposition can
have two negative premises.

Ex.


V        M
No ocean is a country.    (E)         m        V
m No possible relation. M
II. RULES FOR MAKING VALID
CATEGORICAL SYLLOGISMS
   8. At least one premise must be
universal in a valid categorical
syllogism.
Ex.
V        M
Some kids are music-lovers. (I)
Some Filipinos are kids.         (I)         m        V
Some Filipinos are music-lovers. (I)
m No possible relation. 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.                                 “Each & every”   “Some”
All angles are winged-beings.     (A)          V            M
“Some”        “Some”
Some creatures are angles.        (I)
m             V
Some creatures are winged-beings. (I)      “Some”        “Some”
m             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.                                  “Each & every”   “Some”
All angles are winged-beings.      (A)          V            M
“Some”        “Some”
Some creatures are angles.         (I)
m             V
All creatures are winged-beings.   (A)
“ALL”        “Some”
m             M
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       P is M       M is P       P is M
S is M       S is M       M is S       M is S
S is P       S is P       S is P       S is P
(Figure 1)   (Figure 2)   (Figure 3)   (Figure 4)
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         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)
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.
III. THE STANDARD FORMS OF A
VALID CATEGORICAL SYLLOGISM
   Valid forms for the third figure:
Major Premise
A       A        E      E       I      O
Minor Premise
A        I      A        I      A          A
Conclusion
I        I      O       O       I      O
       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).
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.
SUMMARY
   Summarizing all the valid forms, we have the
following table:
Figure   Mood     Figure   Mood   Figure   Mood   Figure   Mood

1        AAA      2        AEE    3        AAI    4        AAI
1        AII      2        AOO    3        AII    4        AEE
1        EAA      2        EAE    3        EAO    4        EAO
1        EII      2        EIO    3        EIO    4        EIO
3        IAI    4        IAI
3        OAO

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