Definition:Categorical Statement

Definition
Let $S$ and $P$ be predicates.

A categorical statement is a statement that can be expressed in one of the following ways in natural language:

In this context, the word is has the meaning of the is of predication:
 * is $P$ means has the property $P$, or belongs to the class of things that have the property $P$
 * is not $P$ means does not have the property $P$, or does not belong to the class of things that have the property $P$.

The word has could equally well be used:
 * has $P$ for is $P$
 * does not have $P$ for is not $P$.

In modern predicate logic, they are denoted as:

In the above:
 * $S \left({x}\right)$ and $P \left({x}\right)$ are propositional functions


 * all $x$ belong to a specified universal of discourse.

Linguistic Note
The letters $A$, $E$, $I$ and $O$ are assigned to the various categorical statements from the first and second vowels to appear in the Latin words AffIrmo (I affirm) and nEgO (I deny).

Also known as
Some sources refer to this as a categorical sentence. However, the word statement is generally preferred as the latter term has a more precise definition.

Also see

 * Definition:Existential Import
 * Definition:Categorical Syllogism


 * Definition:Square of Opposition