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Mediate Inference

Mediate Inference. Mediate Inference. Commonly called as argument Has two major types: Deduction/Deductive Arg./Syllogism Categorical Syllogism Hypothetical Syllogism. Mediate Inference. Induction Induction by complete enumeration Induction incomplete enumeration Induction by analogy.

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Mediate Inference

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  1. Mediate Inference

  2. Mediate Inference • Commonly called as argument • Has two major types: • Deduction/Deductive Arg./Syllogism • Categorical Syllogism • Hypothetical Syllogism

  3. Mediate Inference • Induction • Induction by complete enumeration • Induction incomplete enumeration • Induction by analogy

  4. Categorical Syllogism • is an argument which proceeds from statements concerning the relationship of two terms, to a conclusion concerning the relationship of two terms to each other. • All its propositions are categorical propositions (A,E,I,O).

  5. Example All poets are creative. M P Some artists are poets. S M Ergo, some artists are creative. S P

  6. Ordinary languagearguments No, that girl is not Leyla because she has short hair, while Leyla has long hair. Di laginamodaganngasakyanankay way gasolina Where there’s smoke there’s fire; there’s no fire in the warehouse because there’s no smoke there.

  7. Ordinary languagearguments No, that girl is not Leyla because she has short hair, while Leyla has long hair. No person identical to Leyla is a person who has short hair. All persons identical to that girl are persons who have short hair So, no person identical to that girl is a person identical to Leyla.

  8. Ordinary languagearguments Di laginamodaganngasakyanankay way gasolina. (The car won’t run because it has no gas) All cars without gas are cars that won’t run. All cars identical to that car are cars without gas. So, all cars identical to that car are cars that won’t run.

  9. Ordinary languagearguments Arguments in the ordinary language can be translated to the basic categorical or hypothetical syllogism. Syllogisms (categorical or hypothetical) are basic forms of arguments Hence, the analysis of categorical syllogism

  10. Example All poets are creative. M u + Pp Some artists are poets. Sp + Mp Ergo, some artists are creative. Sp + Pp

  11. Example • Since most 18-year-old lads registered for the Barangay polls and all who are registered for the Barangay polls are voters, then most 18-year-old lads are voters. • All who are registered for the Barangay polls are voters. • Most 18-year-old lads registered for the Barangay polls. • Ergo, most 18-year-old lads are voters. Mu + Pp Sp + Mp Sp + Pp

  12. For Analysis • No legislator has judiciary power. Thus, no senator has judiciary power because they are legislators • No legislator has judiciary power. • Every senator is a legislator. • Thus, no senator has judiciary power. Mu – Pu Su + Mp Su – Pu

  13. For Analysis • Not all religious movements are Christians. Thus, some fundamentalists are Christians because some religious movements are fundamentalists. • Not all religious movements are Christians. • Some religious movements are fundamentalists. • Thus, some fundamentalists are Christians. Mp – Pu Mp + Sp Sp + Pp

  14. Rules of valid syllogism • 1. There must be three and only three terms • 2. The middle term must not occur in the conclusion • 3. The major or minor term may not be universal in the conclusion if it is only particular in the premises • 4. The middle term must be used as a universal at least once. • 5. Two negative premises yield no valid conclusion

  15. Rules of valid syllogism • 6. If both premises are affirmative the conclusion must be affirmative • 7. If one premise is negative the conclusion must be negative • 8. If one premise is particular the conclusion must be particular • 9. From two particular premises no valid conclusion can be draw

  16. Rules of valid syllogism • There must be three and only three terms • possible violation: • Addition: four or more terms • Mandaue is next to Cebu • Consolacion is next to Mandaue • Ergo, Consolacion is next to Cebu • Change in supposition • Man begins with M. • Joseph is a man. • So, Joseph begins with M.

  17. Rules of valid syllogism • Equivocation • A Pail holds water. • This argument holds water. • So, this argument is a pail. • Rule 2. The middle term must not occur in the conclusion • Misplaced middle term • Rule 3. The major or minor term may not be universal in the conclusion if it is only particular in the premise

  18. Rules of Valid syllogism Illicit Minor; Illicit Major Rule 4. The middle term must be used as a universal at least once. -Undistributed middle term Rule 5. Two negative premises yield no valid conclusion -Exclusive premises Rule 6. If both premises are affirmative the conclusion must be affirmative

  19. Rules of Valid syllogism negative conclusion out of affirmative premises Rule 7. If one premise is negative the conclusion must be negative affirmative conclusion out of a negative premise Rule 8. If one premise is particular the conclusion must be particular -universal conclusion out of a particular premise

  20. Rules of Valid syllogism Rule 9. From two particular premises no valid conclusion can be drawn particular premises

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