5 Categorical Syllogisms

1. 5 Categorical Syllogisms 5.2 Venn Diagrams

2. Venn Diagrams For testing Standard Form Categorical Syllogisms we add a circle for the middle term M S S P P

3. Venn Diagrams Follow this procedure diagramming arguments: • Marks are made only for premises • Diagram universal premises first (if both, any order) • Concentrate on the 2 circles talked about in the premise you are diagramming • When reading a diagram, remember that particular statements assert 2 things (existence and location) • When shading, be sure to shade the entire area • Xs go on the line in an area that is unshaded, otherwise they go in the area the shading leaves open • Xs never go on the intersection of 2 lines, and never go on the outside of the circles

4. Venn Diagrams 1 No P are M (see p.246) All S are M No S are P M S P

5. Venn Diagrams 2 All M are P No S are M No S are P M S P

6. Venn Diagrams 3 Some P are M All M are S Some S are P M S P

7. Venn Diagrams Skip a few…

8. Venn Diagrams 5 Some M are P All S are M Some S are P M S P

9. Venn Diagrams 8 Some M are not P Some S are M Some S are not P M S P

10. Venn Diagrams (Aristotelian Standpoint) No F are T All F are C Some C are not T Step 1: Diagram as usual using Boolean Standpoint M S P

11. Venn Diagrams (Aristotelian Standpoint) No F are T All F are C Some C are not T Step 2: Put an X in any circle with just one empty area M S P

12. Venn Diagrams (Aristotelian Standpoint) No F are T All F are C Some C are not T Step 3 Determine whether circled X represents something that actually exists. If it does, the argument is valid from the Aristotelian Standpoint M S P