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:
 * $\map S x$ and $\map P x$ are propositional functions


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

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.

Some sources use the term categorical proposition.

Also see

 * Definition:Existential Import
 * Definition:Categorical Syllogism


 * Definition:Square of Opposition