Modus Bocardo
Form of a syllogism based on the Modus Barbara, in which a negative existential proposition is inferred from another negative existential and a positive universal proposition.
Some M are not P.
All M are S.
Therefore, some S are not P.
For example:
Some rectangles are not squares.
All squares are polygons.
Therefore, some polygons are not squares.
The Modus Bocardo and the Modus Baroco are the only two modes that require an indirect proof of validity in order to be reducible to their general form (the Modus Barbara). In fact, these two modes are identical, except that the premises are in reverse order.
Name
The name “Bocardo” is a mnemonic term that helps to remember the most important characteristics of this mode: The “B” at the beginning indicates that it is related to the Modus Barbara, the two “o” stand for negative existential and the “a” for an affirmative universal statement. The “c” in the name indicates that the transformation to the basic form requires further proof of validity.