Definition:Universal Affirmative

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Definition

A universal affirmative is a categorical statement of the form:

Every $S$ is $P$

where $S$ and $P$ are predicates.


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

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


Its meaning can be amplified in natural language as:

Every object which has the property of being $S$ also has the property of being $P$.


Set Theoretic interpretation of Universal Affirmative

The universal affirmative $\forall x: \map S x \implies \map P x$ can be expressed in set language as:

$\set {x: \map S x} \subseteq \set {x: \map P x}$

or, more compactly:

$S \subseteq P$


Also denoted as

Traditional logic abbreviated the universal affirmative as $\mathbf A$.

Thus, when examining the categorical syllogism, the universal affirmative $\forall x: \map S x \implies \map P x$ is often abbreviated:

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


Also see

  • Results about the universal affirmative can be found here.


Linguistic Note

The abbreviation $\mathbf A$ for a universal affirmative originates from the first vowel in the Latin word Affirmo, meaning I affirm.


Sources

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