====== Modus Darii ======

A form of [[glossary:syllogism|syllogism]] in which a new affirmative existential statement is derived from general and existential statements.

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<h3>Modus Darii</h3>
{{modus_darii.svg?nolink|Modus Darii}}
<figcaption>Type ''AII'', Figure ''1''<span noprint> [[app>#AI1I|Modus Darii]]</span></figcaption>
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> All <abbr "middle term">M</abbr> are <abbr "major term">P</abbr>.
> Some <abbr "minor term">S</abbr> are <abbr "middle term">M</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>.
> Some <var>rhombuses</var> are <var>squares</var>.
> <span conclusio>Therefore, some <var>rhombuses</var> are <var>rectangles</var>.</span>

===== Name =====

The name “Darii” is a [[wp>Mnemonic|mnemonic]] term, in which the vowels (a-i-i) indicate that the first premise is an affirmative [[glossary:universal_quantification|universal quantification]] (type “a”), and that the second premise as well as the conclusion are both affirmative [[glossary:existential_quantification|existential quantifications]] (type “i”).

Although there is an existential statement inferred from a //universal// proposition in this form, no further proof of existence is needed, as the minor statement already implies existence at the intersection of <abbr "minor term">S</abbr> and <abbr "middle term">M</abbr>.

For more information on this naming scheme, and on syllogisms in general, see the article on [[glossary:syllogism|syllogisms]] in the [[glossary:index|glossary]].

===== Variants =====

The following forms are the variants of Modus Darii and can all be transformed back into it:

  * [[logic:inferences:modus_darii:modus_dimatis|Modus Dimatis]]
  * [[logic:inferences:modus_darii:modus_datisi|Modus Datisi]]
  * [[logic:inferences:modus_darii:modus_disamis|Modus Disamis]]
  * [[logic:inferences:modus_darii:modus_darapti|Modus Darapti]]

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

  * [[logic:inferences:modus_barbara:index|Modus Barbara]]
  * [[logic:inferences:modus_celarent:index|Modus Celarent]]
  * [[logic:inferences:modus_ferio:index|Modus Ferio]]

===== More information =====

  * [[wp>Syllogism]] on //Wikipedia//

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