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THE CATEGORICAL SYLLOGISM ARBIND KUMAR SINGH Logical Reasoning Alternative Learning System NEW DELHI

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Topics I. INTRODUCTION Review of categorical propositions II. RULES FOR MAKING VALID CATEGORICAL SYLLOGISMS The 10 rules III. THE STANDARD FORMS OF A VALID CATEGORICAL SYLLOGISM Figures Moods The Valid Forms of Categorical Syllogisms IV. 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: TYPEFORMQUANTITYQUALITYDISTRIBUTION Subject Predicate AAll S is PUniversalAffirmativeDistributed Undistributed ENo S is PUniversalNegativeDistributed ISome S is PParticularAffirmativeUndistributed OSome S is not PParticularNegativeUndistributed 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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Sociable People II. RULES FOR MAKING VALID CATEGORICAL SYLLOGISMS 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 Politicians (Middle Term) Sociable People (Major Term) Councilors (Minor Term) Politicians (Middle Term) Sociable People (Major Term) Councilors (Minor Term) Conclusion First PremiseSecond Premise

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

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

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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) All gamblers Risk-takers Filipinos Some Filipinos who are 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) Mm V 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 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 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 Some M Some m Some V Some 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 ALL m Some M Some m Some V Some M All creatures are winged-beings. (A)

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

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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 AAEE Minor Premise AIAI Conclusion AIEI 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)

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III. THE STANDARD FORMS OF A VALID CATEGORICAL SYLLOGISM Valid forms for the second figure: Major Premise AAEE Minor Premise EOAI Conclusion EOEO 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.

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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 AAEEIO Minor Premise AIAIAA Conclusion IIOOIO

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III. THE STANDARD FORMS OF A VALID CATEGORICAL SYLLOGISM Valid forms for the fourth figure: Major Premise AAEEI Minor Premise AEAIA Conclusion IEOOI 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.

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

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