====== Modus Bamalip ======

A weaker form of the [[logic:inferences:modus_barbara:index|Modus Barbara]], in which only an existential conclusion is inferred. This form has an additional existential requirement.

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<h3>Modus Bamalip</h3>
{{modus_bamalip.svg?nolink|Modus Bamalip}}
<figcaption>Type ''AAI'', Figure ''4''<span noprint> [[app>#AA4I|Modus Bamalip]]</span> \\ Parent: [[logic:inferences:modus_barbara:index|Barbara]]</figcaption>
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> All <abbr "major term">P</abbr> are <abbr "middle term">M</abbr>.
> All <abbr "middle term">M</abbr> are <abbr "minor term">S</abbr>.
>[<i>and there exists at least one</i> <abbr "major term">P</abbr>]*
> <span conclusio>Therefore, some <abbr "minor term">S</abbr> are <abbr "major term">P</abbr>.</span>

For example:

> All <var>squares</var> are <var>rectangles</var>.
> All <var>rectangles</var> are <var>polygons</var>.
> [<i>and there exists at least one</i> square]*
> <span conclusio>Therefore, some <var>squares</var> are <var>polygons</var>.</span>

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* **Note:** When an //existential// conclusion is inferred from //universal// premisses, this requires an (implicit or explicit) [[glossary:existential_import|existential import]], i.e. it must be proven that what the term refers to actually //exists//. In case of the //Modus Bamalip// it is sufficient to prove the existence of the //major term// (<abbr "major term">P</abbr>), as this also implies the existence of <abbr "middle term">M</abbr> and <abbr "minor term">S</abbr>.
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The //Modus Bamalip// is a weaker form of the [[logic:inferences:modus_barbara:index|Modus Barbara]], in which the conclusion is an [[glossary:existential_quantification|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 [[logic:inferences:modus_barbara:modus_barbari|Modus Barbari]], except that //middle term// (<abbr "middle term">M</abbr>) appears in the other positions in the premises.

===== Name =====

The name "Bamalip" is a [[wp>Mnemonic|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 [[logic:inferences:modus_barbara:index|Modus Barbara]], the two "a" for the affirmative [[glossary:universal_quantification|universal]] statements in the premisses and the "i" for the affirmative [[glossary:existential_quantification|existential]] conclusion.

===== See also =====

  * [[glossary:existential_import|Existential import]]
  * [[glossary:existential_quantification|Existential quantification]]
  * [[logic:inferences:modus_barbara:index|Modus Barbara]]
  * [[logic:inferences:modus_barbara:modus_barbari|Modus Barbari]]
  * [[glossary:syllogism|Syllogism]]

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