====== Modus Barbara ======
[[glossary:syllogism|Syllogism]] in which a new general statement is inferred from two [[glossary:universal_quantification|universal quantifications]].
> All M are P.
> All S are M.
> Therefore, all S are P.
For example:
> All rectangles are polygons.
> All squares are rectangles.
> Therefore, all squares are polygons.
===== Name =====
The word "Barbara" is not a name in this context, but rather a [[wp>Mnemonic|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// [[glossary:universal_quantification|universal quantifications]] (type “a”).
For more information on the naming and on syllogisms in general, see the page on [[glossary:syllogism|syllogisms]] in the [[glossary:index|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 "[[logic:inferences:sorites|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:
* [[logic:inferences:modus_barbara:modus_baroco|Modus Baroco]]
* [[logic:inferences:modus_barbara:modus_bocardo|Modus Bocardo]]
* [[logic:inferences:modus_barbara:modus_barbari|Modus Barbari]]
* [[logic:inferences:modus_barbara:modus_bamalip|Modus Bamalip]]
===== See also =====
* [[logic:inferences:sorites|Sorites]]
* [[logic:inferences:modus_celarent:index|Modus Celarent]]
* [[logic:inferences:modus_darii:index|Modus Darii]]
* [[logic:inferences:modus_ferio:index|Modus Ferio]]
===== More information =====
* [[wp>Syllogism]] on //Wikipedia//
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