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Mediate Inference

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Mediate Inference• Commonly called as argument• Has two major types:–Deduction/Deductive

Arg./Syllogism•Categorical Syllogism•Hypothetical Syllogism

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Mediate Inference–Induction

• Induction by complete enumeration

• Induction incomplete enumeration

• Induction by analogy

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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).

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ExampleAll poets are creative. M PSome artists are poets. S M Ergo, some artists are creative. S P

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Ordinary languageargumentsNo, that girl is not Leyla because she has short hair, while Leyla has long hair.Di lagi na modagan nga sakyanan kay way gasolinaWhere there’s smoke there’s fire; there’s no fire in the warehouse because there’s no smoke there.

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Ordinary languageargumentsNo, 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 hairSo, no person identical to that girl is a person identical to Leyla.

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Ordinary languageargumentsDi lagi na modagan nga sakyanan kay 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.

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Ordinary languageargumentsArguments in the ordinary language can be translated to the basic categorical or hypothetical syllogism.Syllogisms (categorical or hypothetical) are basic forms of argumentsHence, the analysis of categorical syllogism

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ExampleAll poets are creative. M u + PpSome artists are poets. Sp + Mp Ergo, some artists are creative. Sp + Pp

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ExampleSince 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

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For AnalysisNo legislator has judiciary power. Thus, no senator has judiciary power because they are legislatorsNo legislator has judiciary power.Every senator is a legislator.Thus, no senator has judiciary power.

Mu – PuSu + MpSu – Pu

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For AnalysisNot 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 – PuMp + SpSp + Pp

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Rules of valid syllogism1. There must be three and only three terms2. The middle term must not occur in the conclusion3. The major or minor term may not be universal in the conclusion if it is only particular in the premises4. The middle term must be used as a universal at least once.5. Two negative premises yield no valid conclusion

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Rules of valid syllogism6. If both premises are affirmative the conclusion must be affirmative7. If one premise is negative the conclusion must be negative8. If one premise is particular the conclusion must be particular9. From two particular premises no valid conclusion can be draw

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Rules of valid syllogismThere must be three and only three terms

possible violation:Addition: four or more termsMandaue is next to CebuConsolacion is next to MandaueErgo, Consolacion is next to CebuChange in suppositionMan begins with M.Joseph is a man.So, Joseph begins with M.

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Rules of valid syllogismEquivocationA 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 termRule 3. The major or minor term may not be universal in the conclusion if it is only particular in the premise

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Rules of Valid syllogismIllicit Minor; Illicit Major

Rule 4. The middle term must be used as a universal at least once.

-Undistributed middle termRule 5. Two negative premises yield no valid conclusion

-Exclusive premisesRule 6. If both premises are affirmative the conclusion must be affirmative

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Rules of Valid syllogismnegative conclusion out of

affirmative premisesRule 7. If one premise is negative the conclusion must be negative

affirmative conclusion out of a negative premiseRule 8. If one premise is particular the conclusion must be particular

-universal conclusion out of a particular premise

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Rules of Valid syllogismRule 9. From two particular premises no valid conclusion can be drawn

particular premises