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**THE CATEGORICAL SYLLOGISM**

ARBIND KUMAR SINGH Logical Reasoning Alternative Learning System NEW DELHI

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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: 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

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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. Sociable People (Major Term) Politicians (Middle Term) Councilors (Minor Term)

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**II. RULES FOR MAKING VALID CATEGORICAL SYLLOGISMS**

Sociable People Politicians 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. “ALL” Animals 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 Filipinos

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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) M m V

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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) M m V No possible relation.

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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) M m V No possible relation.

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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) “Each & every” V “Some” m M

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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: 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)

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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 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)

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**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.

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**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).

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**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.

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**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

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