Fallacy of exclusive premises
A syllogism with of two negative premises has no valid conclusion.
For example ◈:
No polygon is a circle. No rectangle is a circle. ∴ 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.