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 everyday 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, how- ever, 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 proposition (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 infer- ence 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 con- clusion contains an asterisk in the premise.