Definition:Particular Affirmative

From ProofWiki
Jump to: navigation, search

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:

$\exists x: S \left({x}\right) \land P \left({x}\right)$


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 $P$.


Set Theoretic interpretation of Particular Affirmative

The particular affirmative $\exists x: S \left({x}\right) \land P \left({x}\right)$ can be expressed in set language as:

$\left\{{x: S \left({x}\right)}\right\} \cap \left\{{x: P \left({x}\right)}\right\} \ne \varnothing$

or, more compactly:

$S \cap P \ne \varnothing$


Also denoted as

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

Thus, when examining the categorical syllogism, the particular affirmative $\exists x: S \left({x}\right) \land P \left({x}\right)$ is often abbreviated:

$\mathbf I \left({S, P}\right)$


Linguistic Note

$\mathbf I$ originates from the second vowel in the Latin word affIrmo, meaning I affirm.


Also see


Sources