====== Modus Cesaro ======

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 universal premisses.

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<h3>Modus Cesaro</h3>{{modus_cesaro.svg?nolink|Modus Cesaro}}<figcaption>Type ''EAO'', Figure ''2''<span noprint> [[app>#EA2O|Modus Cesaro]]</span> \ Parent: [[logic:inferences:modus_celarent:index|Celarent]]</figcaption>
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> No <abbr "major term">P</abbr> is <abbr "middle term">M</abbr>.
> All <abbr "minor term">S</abbr> are <abbr "middle term">M</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:

> No <i>circle</i> is a <i>rectangle</i>.
> All <i>squares</i> are <i>rectangles</i>.
> [and there exists at least one <i>square</i>]*
> <span conclusio>Therefore, Some <i>squares</i> are not <i>circles</i>.</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 Cesaro// it is sufficient to prove existence for the //minor term// (<abbr "minor term">S</abbr>), as this also implies existence of <abbr "middle term">M</abbr>, while the conclusion does not require existence for <abbr "major term">P</abbr>.</aside>

//Modus Cesaro// is the weaker form of the [[logic:inferences:modus_celarent:modus_cesare|Modus Cesare]], which only infers an existential conclusion. Since every //universal quantification// that does not refer to an empty extension set always implies an //existential quantification//, this variation is possible, but this is of course also a weaker statement than the universal conclusion of the //Modus Cesaro//. 

===== Name =====

The name "Cesaro" 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 "e" and "a" indicate the negative and affirmative [[glossary:universal_quantification|universal]] statements in the premisses and the "o" indicates that the conclusion is a negative [[glossary:existential_quantification|existential]] statement.

===== 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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