The Language of Argument

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C H A P T E R 7 ■ C a t e g o r i c a l L o g i c

Validity for Categorical Arguments

We have introduced Venn diagrams because they provide an efficient and il-

luminating way to test the validity of arguments made up of categorical (A,

E, I, and O) propositions. The basic idea is simple: An argument made up of

categorical propositions is valid if all the information contained in the Venn

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

premises. There are only two ways to put information into a Venn diagram:

We can either shade out an area or put an asterisk in an area. Hence, to test

the validity of an argument made up of categorical propositions, we need

only examine the diagram of the conclusion for its information (its shading

or asterisks) and then check to see if the diagram for the premises contains

this information (the same shading or asterisks).

The following simple example will give a general idea of how this works:

Give two new examples of contexts in which:

1. Stating an A proposition does not seem to commit the speaker to the
   existence of the things to which the subject term refers.


2. Stating an A proposition does not seem to commit the speaker to the
   existence of the things to which the predicate term refers.


3. Stating an E proposition does not seem to commit the speaker to the
   existence of the things to which the subject term refers.


4. Stating an E proposition does not seem to commit the speaker to the
   existence of the things to which the predicate term refers.

Exercise IV

Diagrams

whales mammals

mammals whales

Argument

Some whales are mammals.

Some mammals are whales.

Notice that the only information contained in the diagram for the conclusion

is the asterisk in the overlap between the two circles, and that information is

already included in the diagram for the premise. Thus, the argument is valid.

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