====== Modus Ferio ======

A form of [[glossary:syllogism|syllogism]] in which a new negative existential proposition is derived from a negative universal and an affirmative existential proposition.

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<h3>Modus Ferio</h3>
{{modus_ferio.svg?nolink|Modus Ferio}}
<figcaption>Typ ''EIO'', Form ''1''<span noprint> [[app>#EI1O|Modus Ferio]]</span></figcaption>
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> No <abbr "middle term">M</abbr> is <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 not <abbr "major term">P</abbr>.</span>

For example:

> No <var>square</var> is a <var>circle</var>.
> Some <var>rectangles</var> are <var>squares</var>.
> <span conclusio>Therefore, some <var>rectangles</var> are not <var>circles</var>.</span>

===== Name =====

The name “Ferio” is an artificial word describing the inference scheme: The “e” and “i” stand for a negative and positive  [[glossary:universal_quantification|universal quantifications]], respectively, and the “o” for the negative [[glossary:existential_quantification|existential quantification]] in the conclusion..

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 Ferioand can all be transformed back to it:

  * [[logic:inferences:modus_ferio:modus_festino|Modus Festino]]
  * [[logic:inferences:modus_ferio:modus_ferison|Modus Ferison]]
  * [[logic:inferences:modus_ferio:modus_felapton|Modus Felapton]]
  * [[logic:inferences:modus_ferio:modus_fesapo|Modus Fesapo]]
  * [[logic:inferences:modus_ferio:modus_fresison|Modus Fresison]]

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

  * [[logic:inferences:modus_barbara:index|Modus Barbara]]
  * [[logic:inferences:modus_celarent:index|Modus Celarent]]
  * [[logic:inferences:modus_darii:index|Modus Darii]]

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

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

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