The Language of Argument

1 6 3

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

The same method can be used to test argument forms for validity. The form

of the previous argument and the corresponding diagrams look like this:

Diagrams

S P

P S

Argument Form

Some S are P.

Some P are S.

This argument form is valid, because all the information contained in the

Venn diagram for the conclusion is contained in the Venn diagram for the

premise. And any argument that is a substitution instance of a valid argu-

ment form is valid.

Notice that we did not say that an argument is invalid if it fails these

tests—that is, if some of the information in the Venn diagram for the conclu-

sion (or its form) is not contained in the Venn diagram for the premises (or

their forms). As with truth tables in propositional logic (see Chapter 6), Venn

diagrams test whether arguments are valid by virtue of a certain form, but

some arguments will be valid on a different basis, even though they are not

valid by virtue of their categorical form. Here is one example:

Diagrams

fathers male parents

male parents fathers

Argument

All fathers are male parents.

All male parents are fathers.

The Venn diagram for the conclusion includes shading in the circle for male

parents, whereas the Venn diagram for the premise includes shading in the

circle for fathers, so the premise does not contain the information for the

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