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5.1   Standard Form Mood And Figure
5.1   Standard Form Mood And Figure
5.1   Standard Form Mood And Figure
5.1   Standard Form Mood And Figure
5.1   Standard Form Mood And Figure
5.1   Standard Form Mood And Figure
5.1   Standard Form Mood And Figure
5.1   Standard Form Mood And Figure
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5.1 Standard Form Mood And Figure

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Course lecture I developed over section 5.1 of Patrick Hurley\'s "A Concise Introduction to Logic".

Course lecture I developed over section 5.1 of Patrick Hurley\'s "A Concise Introduction to Logic".

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  • 1. 5.1 Standard form, mood and figure
  • 2. Categorical syllogisms
    • Set of three categorical propositions
      • Two premises and one conclusion
    • Example:
      • All P are M.
      • No S are M.
      • -------------------
      • Therefore, all S are P.
    • Three different terms used in understanding syllogisms
      • Middle term
        • Represented as “M”
      • Major term
        • Predicate of the conclusion
      • Minor term
        • Subject of the conclusion
  • 3. Syllogisms, continued
    • Major premise
      • Contains the major term
    • Minor premise
      • Contains the minor term
    • The major premise comes first, then the minor premise, and finally the conclusion.
      • All P are M. (Major premise)
      • No S are M. (Minor premise)
      • -------------------
      • Therefore, all S are P. (Conclusion)
      • Minor term comes before major term.
  • 4. Syllogisms, continued
    • Mood
      • Made up of the three letters that identify each proposition.
        • Example:
          • AAE – Two A-type premises and one E-type conclusion.
          • AOE – An A-type premise, an O-type premise, and an E-type conclusion
        • Major premise comes before minor premise.
  • 5. Syllogisms, continued
    • Figure
      • Determined by the location of the middle term in the premises.
      • Identified as either 1, 2, 3 or 4.
    • Example:
      • All artists are happy.
      • All writers are artists.
      • ----------------------
      • Therefore, all writers are happy.
      • This is an AAA-1.
        • Artists – Middle term
        • Writers – Minor term
        • Happy – Major term
    S P S P S P S P M S M S S M S M P M M P P M M P Figure 4 Figure 3 Figure 2 Figure 1
  • 6. Syllogisms, continued
    • Once a syllogism can be identified according to its mood and figure, it is possible to determine its validity. (Refer to the tables on page 240.)
      • First, test it from the Boolean standpoint (see if the form appears on the table of unconditionally valid forms).
      • If it does, then it’s unconditionally valid.
      • If it does not, then test it again from the Aristotelian standpoint (refer to the table on conditionally valid forms)
        • Different from the propositions, since now existence is extended to M and P (the middle term and the predicate term) Either S, M, or P has to exist, based on which row the form is in.
  • 7. Syllogisms, continued
    • Examples:
      • (AAI-1) (Conditionally valid, if S exists) (Cats exist, so valid)
      • All mammals are animals. (All M are P)
      • All cats are mammals. (All S are M)
      • --------------------
      • Therefore, some cats are animals. (Some S are P)
      • (EAO-3) (Conditionally valid, if M exists) (Superheroes do not exist, so not valid)
      • (Some superheroes are fast.)
      • (All superheroes are people.)
      • ---------------------
      • Therefore, some people are not fast. (Some S are not P)
  • 8. Syllogisms, continued
      • (AAI-4) (Conditionally valid, if P exists) (Billionaires exist, so valid)
      • All billionaires are happy people. (All P are M)
      • All happy people are movie stars. (All M are S)
      • -----------------------
      • Therefore, some movie stars are billionaires. (Some S are P)
      • (EAE-2) (Unconditionally valid)
      • No people are perfect. (No P are M)
      • All circles are perfect. (All S are M)
      • -----------------------
      • No circles are people. (No S are P)

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