Validity for Categorical Arguments

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 conclusion (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.

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

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 conclusion. Thus, this form of argument is not valid, and some arguments of this form are not valid. Nonetheless, this particular argument is clearly valid, since it is not possible for the premise to be true when the conclusion is false, for the simple reason that the conclusion cannot be false. Because of such cases, Venn diagrams can show us that an argument is valid, but they cannot prove that an argument is invalid.

Despite this limitation, the method of Venn diagrams can be used to test many different kinds of arguments and argument forms for validity. We will show how this method works for two main kinds of argument: immediate inferences and syllogisms.