5 Categorical Syllogisms

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5 Categorical Syllogisms

• 5.4 Reducing the Number of Terms

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Reducing the Number of Terms

• This section is really just about using
  Conversion, Obversion, and Contraposition to get
  arguments into standard form.
• Lets review what these operations work on
• Conversion (E and I)
• Obversion (A, E, I, and O)
• Contraposition (A and O)

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Reducing the Number of Terms

• All P are non-W
• Some E are W
• Some non-P are not non-E
• How many terms are there? ____
• How many can there be in a Standard Form
  Categorical Syllogism? ____
• How can we fix the argument? ____

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Reducing the Number of Terms

• On premise one, what operation will result in a
  logically equivalent form, while reducing the
  number of terms in the argument?

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Reducing the Number of Terms

• All P are non-W --- obversion ---gt No P are W
• Cool.
• How about the conclusion,
• Some non-P are not non-E ?
• What would get rid of the complexity?

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Reducing the Number of Terms

• Some non-P are not non-E --- Contraposition ---gt
  Some E are not P
• So, putting the argument back together,

All P are non-W Some E are W Some non-P are not
non-E
No P are W Some E are W Some E are not P
Obversion ? Contraposition ?
Test this argument using Venn or 5 Rules