TESTING SYLLOGISMS FOR VALIDITY

To test the validity of a syllogism us- ing a Venn diagram, we first fill in the diagram to indicate the information contained in the premises. Remember that the only information contained in a Venn diagram is indicated either by shading out an area or by putting an asterisk in it. The argument is valid if the information expressed by the conclusion is already contained in the diagram for the premises.2 To see this, consider the diagrams for examples that we have already given:

All rectangles have four sides. All squares are rectangles.

All squares have four sides.

Here’s the diagram for the premises:

Squares

Rectangles

Things having four sides

This diagram for the conclusion contains only the information that nothing is in the circle for squares that is not also in the circle for things having four sides. In the diagram for the premises, all the things that are squares are cor- ralled into the region of things that have four sides. Thus, the diagram for the premises contains all of the information in the diagram for the conclusion. That shows that this syllogism is valid.

Next, let’s try a syllogism with a negative premise:

No ellipses have sides. All circles are ellipses.

No circles have sides.

Here’s the diagram for the premises:

Squares Things having four sides

Here’s the diagram for the conclusion:

Circles

Ellipses