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.

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.

• Syllogism – underlying form of inference.
• Affirmative conclusion from a negative premise – Similar form of fallacy.
• Fallacy of exclusive premises – Reversal of this form of fallacy.

• Negative conclusion from affirmative premises on Wikipedia
• Negative Conclusion from Affirmative Premises on Logically Fallacious
• Negative Conclusion from Affirmative Premisses on Fallacy Files