# Definition:Particular Negative

## Contents

## 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 $P$.*

### Set Theoretic interpretation of Particular Negative

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

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

or, more compactly:

- $S \cap \complement \left({P}\right) \ne \varnothing$

## 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 **neg O**, meaning

**I deny**.

## Also see

## Sources

- 1965: E.J. Lemmon:
*Beginning Logic*... (previous) ... (next): $\S 4.4$: The Syllogism - 1973: Irving M. Copi:
*Symbolic Logic*(4th ed.) ... (previous) ... (next): $4.1$: Singular Propositions and General Propositions