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:


 * $\forall x: \map S x \implies \neg \map P x$

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 $\forall x: \map S x \implies \neg \map P x$ is often abbreviated:
 * $\map {\mathbf E} {S, P}$

Also see

 * Definition:Square of Opposition


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


 * Equivalence of Definitions of Universal Negative