Fallacy of exclusive premises

A syllogism with of two negative premises has no valid conclusion.

For example Open in Syllogism-Finder App:

No polygon is a circle.
No rectangle is a circle.
Therefore, no rectangle is a polygon.

Negative statements have much less descriptive power than positive ones – we learn less about A from the statement “A is not a tree” than from the statement “A is a house”. Therefore, there are a number of restrictions on what can be done with negative statements.

Even with only a single negative premise, it is no longer possible to draw any positive conclusion (affirmative conclusion from a negative premise).

If both premises are negative, there are no ways in which the middle term can reliably connect the statements. Therefore, it is not possible to infer a conclusion which connects the major and minor terms. In other words: it is not possible to draw a conclusion.

• Affirmative conclusion from a negative premise – even a single negative premise means no affirmative conclusion can be drawn
• Negative conclusion from affirmative premises – only affirmative premisses don’t allow a negative conclusion
• Syllogism – underlying form of inference.

• Fallacy of exclusive premises on Wikipedia
• Exclusive Premises on Logically Fallacious
• Exclusive Premisses on Fallacy Files
• Syllogistic Fallacies: Exclusive Premisses on the servers of Lander University