Laws of Conversion

Theorem

Law of Simple Conversion of $\mathbf I$

Consider the particular affirmative categorical statement Some $S$ is $P$:

$\map {\mathbf I} {S, P}: \exists x: \map S x \land \map P x$

Then Some $P$ is $S$:

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

Law of Simple Conversion of $\mathbf E$

Consider the universal negative categorical statement No $S$ is $P$:

$\map {\mathbf E} {S, P}: \forall x: \map S x \implies \neg \map P x$

Then No $P$ is $S$:

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

Sources

• 1965: E.J. Lemmon: Beginning Logic ... (previous) ... (next): Chapter $4$: The Predicate Calculus $2$: $4$ The Syllogism