Definition:Categorical Statement/Abbreviation

Definition

Let $S$ and $P$ be predicates.

A categorical statement connecting $S$ and $P$ can be presented in abbreviated form as:

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

where $\mathbf \Phi$ is one of either $\mathbf A$, $\mathbf E$, $\mathbf I$ or $\mathbf O$, signifying Universal Affirmative, Universal Negative, Particular Affirmative and Particular Negative respectively.

Thus:

						\(\ds \map {\mathbf A} {S, P} \)	denotes	All $S$ are $P$
						\(\ds \map {\mathbf E} {S, P} \)	denotes	No $S$ are $P$
						\(\ds \map {\mathbf I} {S, P} \)	denotes	Some $S$ are $P$
						\(\ds \map {\mathbf O} {S, P} \)	denotes	Some $S$ are not $P$

Linguistic Note

The letters $A$, $E$, $I$ and $O$ are assigned to the various categorical statements from the first and second vowels to appear in the Latin words:

AffIrmo (I affirm)

nEgO (I deny).

Sources

• 1973: Irving M. Copi: Symbolic Logic (4th ed.) ... (previous) ... (next): $4$: Propositional Functions and Quantifiers: $4.1$: Singular Propositions and General Propositions
• 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): syllogism
• 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): syllogism