All M are P. All S are M. ∴ All S are P.
All rectangles are polygons. All squares are rectangles. ∴ All squares are polygons.
The word “Barbara” is not a name in this context, but rather a mnemonic term in which the vowels (a-a-a) indicate that all three statements, i.e. the two premises as well as the conclusion, are all affirmative universal quantifications (type “a”).
Instead of the usual two premises, there is in principle no limit to the number of conditional statements that can be chained to reach a conclusion. Such a sequence of conditionals “stacked” together is also called a “Sorites”, from the Greek word for “heap”.
Conversely, the Modus Barbara could also be considered a special case of the sorites with exactly three terms in two premises.
All of the following variants can be transformed into a valid Modus Barbara. However, the first two (Baroco and Bocardo) require further proof of validity for this transformation:
- Syllogism on Wikipedia