No Valid Categorical Syllogism contains two Negative Premises
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Theorem
No categorical syllogism of which both premises are negative categorical statements is valid.
Proof
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Historical Note
This rule of quality was axiomatic at the time of Aristotle, when the theory of the categorical syllogism was initially developed.
Sources
- 1965: E.J. Lemmon: Beginning Logic ... (previous) ... (next): Chapter $4$: The Predicate Calculus $2$: $4$ The Syllogism