====== 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.
> All P are M.
> No M is S.
>[and there exists at least one S]*
> Therefore, some S are not P.
For example:
> All squares are rectangles.
> No rectangle is a circle.
> [and there exists at least one circle]*
> Therefore, some circles are not squares.
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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