1. 5 Categorical Syllogisms
5.4 Reducing the Number of Terms

2. Reducing the Number of Terms
This section is really just about using Conversion, Obversion, and Contraposition to get arguments into standard form. Let’s review what these operations work on: Conversion (E and I) Obversion (A, E, I, and O) Contraposition (A and O)

3. 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? ____

4. 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?

5. Reducing the Number of Terms
All P are non-W --- obversion ---> No P are W Cool. How about the conclusion, Some non-P are not non-E ? What would get rid of the complexity?

6. Reducing the Number of Terms
Some non-P are not non-E --- Contraposition ---> 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
Obversion 
Contraposition 
No P are W
Some E are W
Some E are not P
Test this argument using Venn or 5 Rules