Rules of Quality
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Theorem
Conclusion of Valid Categorical Syllogism is Negative iff one Premise is Negative
The conclusion of a valid categorical syllogism is negative if and only if one of the premises is also negative.
No Valid Categorical Syllogism contains two Negative Premises
No categorical syllogism of which both premises are negative categorical statements is valid.
Also see
Historical Note
The rules of quality were 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: Exercises: $\text{B}$: Rules of Quality