5 Categorical Syllogisms 5.2 Venn Diagrams

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

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

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

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

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

Venn Diagrams Skip a few…

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

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

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 S P M

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 S P M

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 S P M