# Modus Barbara

Syllogism in which a new general statement is inferred from two universal quantifications.

All M are P.

All S are M.

Therefore, all S are P.

For example:

Allrectanglesarepolygons.

Allsquaresarerectangles.

Therefore, allsquaresarepolygons.

## Name

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”).

For more information on the naming and on syllogisms in general, see the page on syllogisms in the glossary.

## Sorites

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.

## Variants

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:

## See also

## More information

- Syllogism on
*Wikipedia*