Definition:Particular Negative

Definition
A particular negative is a categorical statement of the form:
 * Some $S$ is not $P$

where $S$ and $P$ are predicates.

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


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

Its meaning can be amplified in natural language as:
 * There exists at least one object with the property of being $S$ which does not have the quality of being $P$.

Also denoted as
Traditional logic abbreviated the particular negative as $\mathbf O$.

Thus, when examining the categorical syllogism, the particular negative $\exists x: \map S x \land \neg \map P x$ is often abbreviated:
 * $\map {\mathbf O} {S, P}$

Linguistic Note
$\mathbf O$ originates from the second vowel in the Latin word negO, meaning I deny.

Also see

 * Definition:Square of Opposition


 * Definition:Universal Affirmative
 * Definition:Universal Negative
 * Definition:Particular Affirmative


 * Equivalence of Definitions of Particular Negative