Law of Simple Conversion of I
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Theorem
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 $S$:
- $\map {\mathbf I} {P, S}$
Proof
| \(\ds \) | \(\) | \(\ds \map {\mathbf I} {S, P}\) | ||||||||||||
| \(\ds \leadsto \ \ \) | \(\ds \exists x: \, \) | \(\ds \) | \(\) | \(\ds \map S x \land \map P x\) | Definition of Particular Affirmative | |||||||||
| \(\ds \leadsto \ \ \) | \(\ds \exists x: \, \) | \(\ds \) | \(\) | \(\ds \map P x \land \map S x\) | Conjunction is Commutative | |||||||||
| \(\ds \leadsto \ \ \) | \(\ds \) | \(\) | \(\ds \map {\mathbf I} {P, S}\) | Definition of Particular Affirmative |
$\blacksquare$
Sources
- 1965: E.J. Lemmon: Beginning Logic ... (previous) ... (next): Chapter $4$: The Predicate Calculus $2$: $4$ The Syllogism