====== Modus Calemos ======

Form of a [[glossary:syllogism|syllogism]] based on the [[logic:inferences:modus_celarent:index|Modus Celarent]], in which a negative [[glossary:existential_quantification|existential]] proposition is inferred from positive and negative [[glossary:universal_quantification|universal]] premisses.

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<h3>Modus Calemos</h3>
{{modus_calemos.svg?nolink|Modus Calemos}}
<figcaption>Type ''AEO'', Figure ''4''<span noprint> [[app>#AE4O>|Modus Calemos]]</span> \\ Parent: [[logic:inferences:modus_celarent:index|Celarent]]</figcaption>
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> All <abbr "major term">P</abbr> are <abbr "middle term">M</abbr>.
> No <abbr "middle term">M</abbr> is <abbr "minor term">S</abbr>.
>[<i>and there exists at least one</i> <abbr "minor term">S</abbr>]*
> <span conclusio>Therefore, some <abbr "minor term">S</abbr> are not <abbr "major term">P</abbr>.</span>

For example:

> All <var>squares</var> are <var>rectangles</var>.
> No <var>rectangle</var> is a <var>circle</var>.
> [<i>and there exists at least one</i> circle]*
> <span conclusio>Therefore, some <var>circles</var> are not <var>squares</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 Calemos// it is sufficient to prove the existence of the //minor term// (<abbr "minor term">S</abbr>), as the conclusion does not actually imply the existence of <abbr "middle term">M</abbr> and/or <abbr "major term">P</abbr>.
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The //Modus Calemos// is a weaker form of the [[logic:inferences:modus_celarent:modus_calemes|Modus Calemes]], in which the conclusion is an [[glossary:existential_quantification|existential]] rather than a universal statement. This is possible since every universal quantification that does not refer to an //empty extension set// always implies an //existential quantification//, but this is of course also a weaker statement than the universal conclusion of the //Modus Calemes//.

===== Name =====

The name "Calemos" is a [[wp>Mnemonic|mnemonic]] term that helps to remember the most important character­istics of this mode: The "C" at the beginning indicates that it is related to the [[logic:inferences:modus_celarent:index|Modus Celarent]], the "a" and "e" indicates the affirmative and negative [[glossary:universal_quantification|universal]] premisses, and the "o" that there is a negative [[glossary:existential_quantification|existential]] conclusion.

==== Alternative name ====

  * Modus Calemop

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

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

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