Definition:Particular Affirmative

Definition

A particular affirmative is a categorical statement of the form:

Some $S$ is $P$

where $S$ and $P$ are predicates.

In the language of predicate logic, this can be expressed as:

$\exists x: \map S x \land \map P x$

Its meaning can be amplified in natural language as:

There exists at least one object with the property of being $S$ which also has the quality of being $P$.

The particular affirmative $\exists x: \map S x \land \map P x$ can be expressed in set language as:

$\set {x: \map S x} \cap \set {x: \map P x} \ne \O$

or, more compactly:

$S \cap P \ne \O$

Traditional logic abbreviated the particular affirmative as $\mathbf I$.

Thus, when examining the categorical syllogism, the particular affirmative $\exists x: \map S x \land \map P x$ is often abbreviated:

$\map {\mathbf I} {S, P}$

The abbreviation $\mathbf I$ for a particular affirmative originates from the second vowel in the Latin word affIrmo, meaning I affirm.