Definition:Universal Negative

Definition
A universal negative is a categorical statement of the form:
 * No $S$ is $P$

where $S$ and $P$ are predicates.

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


 * $\forall x: S \left({x}\right) \implies \neg P \left({x}\right)$

Its meaning can be amplified in natural language as:
 * Given any arbitrary object, if it has the property of being $S$, then it does not have the quality of being $P$.

Also denoted as
Traditional logic abbreviated the universal negative as $\mathbf E$.

Thus, when examining the categorical syllogism, the universal negative $\forall x: S \left({x}\right) \implies \neg P \left({x}\right)$ is often abbreviated:
 * $\mathbf E \left({S, P}\right)$

Linguistic Note
$\mathbf E$ originates from the first vowel in the Latin word nEgo, meaning I deny.

Also see

 * Definition:Square of Opposition


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


 * Equivalence of Definitions of Universal Negative