The Language of Argument

1 6 9

V a l i d i t y f o r C a t e g o r i c a l A r g u m e n t s

TesTing syllogisms for ValiDiTy.  To test the validity of a syllogism using 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 con-

tained 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

Here’s the diagram for the conclusion:

Squares 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 conclu-

sion. 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:

Circles

Ellipses

Things having sides

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