====== Modus Barbara ======

[[glossary:syllogism|Syllogism]] in which a new general statement is inferred from two [[glossary:universal_quantification|universal quantifications]].

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<h3>Modus Barbara</h3>
{{modus_barbara.svg?nolink|Modus Barbara}}
<figcaption>Type ''AAA'', Figure ''1''<span noprint>[[app>#AA1A|Modus Barbara]]</span></figcaption>
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> All <abbr "middle term">M</abbr> are <abbr "major term">P</abbr>.
> All <abbr "minor term">S</abbr> are <abbr "middle term">M</abbr>.
> <span conclusio>Therefore, all <abbr "minor term">S</abbr> are <abbr "major term">P</abbr>.</span>

For example:

> All <var>rectangles</var> are <var>polygons</var>.
> All <var>squares</var> are <var>rectangles</var>.
> <span conclusio>Therefore, all <var>squares</var> are <var>polygons</var>.</span>

===== 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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