Modus Barbari

A weaker form of the Modus Barbara, in which only an existential conclusion is inferred. This form has an additional existential requirement.

All M are P.

All S are M.

[and there exists at least one S]*

∴ Some S are P.

For example:

All rectangles are polygons.

All squares are rectangles.

[and there exists at least one square ]*

∴ Some squares are polygons.

* Note: When an existential conclusion is inferred from universal premisses, this requires an (implicit or explicit) existential import, i.e. it must be proven that what the term refers to actually exists. In case of the Modus Barbari it is sufficient to prove the existence of the minor term (S), as this also implies the existence of M and P.

The Modus Bamalip is a weaker form of the Modus Barbara, in which the conclusion is an existential rather than a universal statement. Since every universal quantification that does not refer to an empty extension set always implies an existential quantification, this variation is possible, but this is of course also a weaker statement than the universal conclusion of the Modus Barbara.

Moreover, this form resembles the Modus Bamalip, except that middle term (M) appears in the other positions in the premises.

The name “Barbari ” 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 “a” for the affirmative universal statements in the premisses and the “i” for the affirmative existential conclusion.

• Existential import
• Existential quantification
• Modus Barbara
• Modus Bamalip
• Syllogism