Rules of Quantity
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Theorem
Distributed Term of Conclusion of Valid Categorical Syllogism is Distributed in Premise
Let $T$ be a term of the conclusion $C$ of a valid categorical syllogism $Q$.
Let $T$ be distributed in $C$.
Then $T$ is also distributed in whichever premise of $Q$ in which it appears.
Middle Term of Valid Categorical Syllogism is Distributed at least Once
Let $M$ be the middle term of a valid categorical syllogism $Q$.
Then $M$ is distributed in at least one of the premises of $Q$ in which it appears.
Also see
Historical Note
The Rules of Quantity 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: $\text{A}$: Rules of Quantity