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Negative conclusion from affirmative premises

A formal fallacy, in particular in syllogisms, where a negative conclusion is (erroneously) inferred from affirmative premises.

For example Open in Syllogism-Finder App:

All squares are rectangles.
All rectangles are tetragons.
Therefore, Some tetragons are not squares.


In principle, no negative conclusions can be drawn from exclusively affirmative (positive) premises. Therefore, a negative conclusion from exclusively affirmative premises is invalid.

When are such conclusions valid

In a certain cases, affirmative statements (especially all-propositions) can be transformed into negative statements (e.g. “all A are B ” is equivalent to “no A is not-B ”). However, this should be done before formulating the inference and not implicitly.

See also

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