THE CATEGORICAL SYLLOGISM

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THE CATEGORICAL SYLLOGISM

• Michael Jhon M. Tamayao, M.A. Phil.
• LOGIC
• College of Medical Technology
• Cagayan State University

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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

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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.

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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
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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.

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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
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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)
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II. RULES FOR MAKING VALID CATEGORICAL SYLLOGISMS
Councilors
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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.

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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.

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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
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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
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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.

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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.
Cats
Pigs
Some animals
Some animals
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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
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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)

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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
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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)

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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)

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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)

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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)

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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
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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.

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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.

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III. THE STANDARD FORMS OF A VALID CATEGORICAL
SYLLOGISM

• FIGURES

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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.

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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
• The major premise must be universal. (A or E)
• The minor premise must be affirmative. (A or I)

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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
• The major premise must be universal. (A or E)
• At least one premise must be negative.

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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
• The minor premise must be affirmative (A or I).
• The conclusion must be particular (I or O).

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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
• 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.

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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