The Language of Argument

1 5 5

C a t e g o r i c a l P r o p o s i t i o n s

These forms are called categorical forms, and propositions with these forms

are called categorical propositions.

As with the propositional forms discussed in the previous chapter, the A,

E, I, and O forms for categorical propositions are not themselves proposi-

tions, so they are neither true nor false. Instead, they are patterns for whole

groups of propositions. We get propositions from these forms by uniformly

replacing the variables S and P with terms that refer to classes of things.

For example, “Some spies are not aliens” is a substitution instance of the O

propositional form. Nonetheless, we will refer to propositions with the A,

E, I, or O form simply as A, E, I, or O propositions, except where this might

cause confusion.

A and E propositions are said to be universal propositions (because they

are about all S), and I and O propositions are called particular propositions

(because they are about some S). A and I propositions are described as affirm-

ative propositions (because they say what is P), and E and O propositions are

referred to as negative propositions (because they say what is not P). Thus,

these four basic propositional forms can be described this way:

A = Universal Affirmative E = Universal Negative

I = Particular Affirmative O = Particular Negative

These four forms fit into the following table:

Affirmative  Negative

Universal    A: All S is P.  E: No S is P.

Particular   I: Some S is P.     O: Some S is not P.

Here are the Venn diagrams for the four basic categorical forms:

S P S P

S P

A: All S is P. E: No S is P.

I: Some S is P. O: Some S is not P.

S P

These basic categorical forms, together with their labels, classifications, and

diagrams, should be memorized, because they will be referred to often in

the rest of this chapter.

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