# 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): $\S 4.4$: The Syllogism: Exercises: $\text{B}$: Rules of Quality