====== Modus Fesapo ======

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

<aside float-right>
<figure>
<h3>Modus Fesapo</h3>
{{modus_fesapo.svg?nolink|Modus Fesapo}}
<figcaption>Type ''EAO'', Figure ''4''<span noprint> [[app>#EA4O|Modus Fesapo]]</span> \\ Parent: [[logic:inferences:modus_ferio:index|Ferio]]</figcaption>
</figure>
</aside>

> No <abbr title="major term">P</abbr> is <abbr title="middle term">M</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 not <abbr title="major term">P</abbr>.</span>

For example:

> No <var>circle</var> is a <var>square</var>.
> All <var>squares</var> are <var>rectangles</var>.
> [and there exists at least one <var>square</var>]*
> <span conclusio>Therefore, Some <var>rectangles</var> are not <var>circles</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 Fesapo// it is sufficient to prove existence for the //middle term// (<abbr title="middle term">M</abbr>), as this also implies existence for <abbr title="minor term">S</abbr>, whereas, in this particular case, actual existence for <abbr title="major term">P</abbr> is not implied.
</aside>

===== Name =====

The name "Fesapo" is a [[wp>Mnemonic|mnemonic]] term that helps to remember the most important characteristics of this mode: The "F" at the beginning indicates that it is related to the [[logic:inferences:modus_ferio:index|Modus Ferio]], while the vowels indicate the types of statements used in the form: "e" and "a" stand for a //negative// and //affirmative// [[glossary:universal_quantification|universal]] premisses and the "o" for a negative [[glossary:existential_quantification|existential]] conclusion.

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

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

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