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