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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 &quot;A Concise Introduction to Logic&quot;.

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

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### Transcript

• 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)