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

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.

Categorical Immediate Inferences

A categorical immediate inference is an argument with the following features:

1. It has a single premise. (That is why the inference is called immediate.)


2. It is constructed from A, E, I, and O propositions. (That is why the
   inference is called categorical.)
   These arguments deserve attention because they occur quite often in every-
   day reasoning.
   We will focus on the simplest kind of immediate inference, which is con-
   version. We convert a proposition (and produce its converse) simply by revers-
   ing the subject term and the predicate term. By the subject term, we mean the
   term that occurs as the grammatical subject; by the predicate term, we mean
   the term that occurs as the grammatical predicate. In the A proposition “All
   spies are aliens,” “spies” is the subject term and “aliens” is the predicate
   term; the converse is “All aliens are spies.”
   In this case, identifying the predicate term is straightforward because the
   grammatical predicate is a noun—a predicate nominative. Often, however,
   we have to change the grammatical predicate from an adjective to a noun
   phrase in order to get a noun that refers to a class of things. “All spies are
   dangerous” becomes “All spies are dangerous things.” Here “spies” is the
   subject term and “dangerous things” is the predicate term. Although this
   change is a bit artificial, it is necessary because, when we convert a proposi-
   tion (that is, reverse its subject and predicate terms), we need a noun phrase
   to take the place of the grammatical subject. In English we cannot say, “All
   dangerous are spies,” but we can say, “All dangerous things are spies.”
   Having explained what conversion is, we now want to know when this
   operation yields a valid immediate inference. To answer this question, we use
   Venn diagrams to examine the relationship between each of the four basic
   categorical propositional forms and its converse. The immediate inference
   is valid if the information contained in the conclusion is also contained in
   the premise—that is, if any region that is shaded in the conclusion is shaded
   in the premise, and if any region that contains an asterisk in the conclusion
   contains an asterisk in the premise.

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