001 logic09_syllogism

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001 logic09_syllogism

  1. 1. SYLLOGISMTerms, Premises, Figuresand Moods
  2. 2. SYLLOGISM (…meaning)• 6.1. Syllogism -- adeductive argument inwhich a conclusion isinferred from twopremises
  3. 3. Categorical S…• Categorical Syllogism is adeductive argumentconsisting of threecategorical propositions thattogether contain exactlythree terms, each of whichoccurs in exactly two of theconstituent propositions
  4. 4. Conclusion…• Conclusion of a standard-formsyllogism is a standard-formcategorical proposition thatcontains two of the syllogism’sthree terms. The conclusion isalways used to identify theterms of the syllogism
  5. 5. The Three Terms…• 6.2. The Three Terms: (1) MajorTerm -- predicate of theconclusion; symbolized by P; (2)Minor Term -- the subject term ofthe conclusion; symbolized by S;(3) Middle Term -- third term ofthe syllogism, which does notoccur in the conclusion,appearing instead in bothpremises; symbolized by M
  6. 6. Premises…• 6.3. Premises: Major premise containsthe major term while Minor premisecontains the minor term• 6.4. The Law of All and the Law of None:• 6.4.1. The Law of All states: “What isaffirmed of a logical whole may beaffirmed of a logical part of that whole.”• Example: Insects are worth-watching;Butterflies are insects; Therefore,butterflies are worth watching.
  7. 7. Law of None• 6.4.2. The Law of None states:“What is denied of a logicalwhole may be denied of alogical part of that whole.”• Example: All Africans are notCaucasians; St. Augustine isan African; Therefore, St.Augustine is not Caucasian
  8. 8. General Rules…• 6.5. General rules for valid syllogisms• 6.5.1. Only three terms may appear in the syllogism, each ofwhich is used in the same sense throughout the argument.• 6.5.2. Neither the major nor minor term may be a universal inthe conclusion, if it was only a particular term in the premises.If the minor term or major term in the premises is not thesame in quantity in the conclusion, the fallacies committed areeither fallacy of illicit minor or the fallacy of illicit major.• Example of a Syllogism with Illicit Major:• Every teacher is professional• Mr. John Foster is not a teacher• Therefore, Mr. John Foster is not professional.• Example of a Syllogism with Illicit Minor:• All Varsity players are scholars• All Varsity players are not medical students• Therefore, all medical students are scholars.
  9. 9. Cont’n…• 6.5.3.The middle term may not appear in theconclusion.• 6.5.4. The middle term must be distributed at leastonce in the premises, that is, used as a universal.Violation of this rule is called Fallacy of theUndistributed Middle Term.• 6.5.5. If both premises are affirmative, theconclusion must also be affirmative.• 6.5.6. Both premises may not be negative; one atleast must be affirmative. Failure to abide by thisrule is called Fallacy of Two Negative premises.• Example:• All villages are not safe;• All commercial districts are not villages;• Therefore, all commercial districts are not safe.
  10. 10. Cont’n…• 6.5.7. If either premise is negative,the conclusion must be negativeotherwise you draw an affirmativeconclusion which is invalid. Fallacy ofDrawing an Affirmative Conclusionfrom a Negative Premise iscommitted when the above rule isviolated.• Example:• Traditions are not modern;Observance of Lent is a tradition;Therefore, observance of Lent ismodern.
  11. 11. Cont’n…• 6.5.8. No conclusion can be drawnfrom two particular premises; one atleast must be a universalproposition.• Example: Some beaches are cleanand fresh;• Some beaches are located far away;• Therefore, some located far awayplaces are clean and fresh.• Existential Fallacy is committed whenthe rule is not observed.
  12. 12. Figures and Moods…• Figures and Moods ofCategorical Syllogism. Thefigure of a syllogism indicatesthe position of the middle termin the premises.• The mood of a standard-formsyllogism is determined by thetypes (identified by letter: A, E,I or O) of the standard-formcategorical propositions
  13. 13. Cont’n…• The following are the valid figures and theircorresponding moods of syllogisms:• Figure 1 Figure 2 Figure 3 Figure 4• M P P M M P P M• S M S M M S M S• S P S P S P S P
  14. 14. Cont’n…• Figure 1: AAA, EAE, AII, EIO• Examples:•• Figure 1 – AAA: All drivers are licensed; Allmessengers are drivers;Therefore, all messengers arelicensed• Figure 1 – EAE: No animals are worthless; All cats areanimals; Therefore, No cats are worthless.• Figure 1 – AII: All Christians are baptized; SomeChinese are Christians; Therefore, some Chinese arebaptized.• Figure 1 – EIO: All employees are not discriminated;Some accountants are employees; Therefore, someaccountants are not discriminated.
  15. 15. Cont’n…• Figure 2: EAE, AEE, EIO, AOO• Figure 2 – EAE: No squatters are rich; Allexecutives are rich;Therefore, all executivesare not squatters.• Figure 2 – AEE: All terrorists are bad people;No seminarians are bad people; Therefore, noseminarians are terrorists.• Figure 2 – EIO: No children are burdensome;Some lawless elements are burdensome;Therefore, some lawless elements are notchildren.• Figure 2 – AOO: Every school administrator isa responsible person; Some workers are notresponsible persons; Therefore, some workersare not school administrators.
  16. 16. Cont’n…• Figure 3: IAI, AII, EIO Examples:• Figure 3 – IAI: Some nursing studentsare scholars; All nursing students arelaw-abiding citizens; Therefore, somelaw-abiding citizens are scholars.• Figure 3 – AII: All passengers are safe;Some passengers are children;Therefore, some children are safe.• Figure 3 – EIO: No activists areviolent; Some activists are students;Therefore, some students are notviolent2nd TO THE LAST SLIDE
  17. 17. Cont’n…• Figure 4: AEE, IAI, EIOExamples:• Figure 4 – AEE: All boxers are brave individuals; Allbrave individuals are homosexuals; Therefore, allhomosexuals are not boxers.• Figure 4 – IAI• Some chefs are internationally known people• All internationally known people are respectedones• Therefore, some respected ones are chefs.• Figure 4 – EIO• All utensils are not imported items• Some imported items are costly goods• Therefore, some costly goods are not utensils.•END OF THETOPIC
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