====== Modus Darapti ======

Form of a [[glossary:syllogism|syllogism]] based on the [[logic:inferences:modus_darii:index|Modus Darii]], in which an affirmative [[glossary:existential_quantification|existential]] proposition is inferred from two affirmative [[glossary:universal_quantification|universal]] premisses. This form has an additional existential requirement. 

<aside float-right>
<figure>
<h3>Modus Darapti</h3>
{{modus_darapti.svg?nolink|Modus Darapti}}
<figcaption>Typ ''AAI'', Form ''3''<span noprint> [[app>#AA3I|Modus Darapti]]</span> \\ Parent: [[logic:inferences:modus_darii:index|Darii]]</figcaption>
</figure>
</aside>

> All <abbr title="middle term">M</abbr> are <abbr title="major term">P</abbr>.
> All <abbr title="middle term">M</abbr> are <abbr title="minor term">S</abbr>.
> [<i>and there exists at least one</i> <abbr title="middle term">M</abbr>]*
> <span conclusio>Therefore, Some <abbr title="minor term">S</abbr> are <abbr title="major term">P</abbr>.</span>

For example:

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

<aside box>
* **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 Darapti// it is sufficient to prove existence for the //middle term// (<abbr title="middle term">M</abbr>), as this also implies existence of both <abbr title="minor term">S</abbr> and <abbr title="major term">P</abbr>.
</aside>

//Modus Disamis// is very similar to the modi [[logic:inferences:modus_darii:modus_datisi|Datisi]] and [[logic:inferences:modus_darii:modus_disamis|Disamis]], except that it is based on two //universal// statements in the premisses, rather than a //universal// and an //existential// statement each.

===== Name =====

The name "Darapti" is a [[wp>Mnemonic|mnemonic]] term that helps to remember the most important characteristics of this mode: The "D" at the beginning indicates that it is related to the [[logic:inferences:modus_darii:index|Modus Darii]], the two "a" and the "i" indicate that affirmative [[glossary:universal_quantification|universal]] and [[glossary:existential_quantification|existential]] statements make up this form.

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

  * [[glossary:existential_import|Existential import]]
  * [[glossary:existential_quantification|Existential quantification]]
  * [[logic:inferences:modus_darii:index|Modus Darii]]
  * [[glossary:syllogism|Syllogism]]
  * [[glossary:universal_quantification|Universal quantification]]

{{page>templates:banner#Short-BG-Logic&noheader&nofooter}}