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| logic:inferences:modus_celarent:modus_cesaro [25.05.22, 21:59:19] – ↷ Links adapted because of a move operation admin | logic:inferences:modus_celarent:modus_cesaro [27.05.22, 10:56:04] – ↷ Links adapted because of a move operation 154.54.249.205 |
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| ====== Modus Cesaro ====== | ====== Modus Cesaro ====== |
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| Form of a [[glossary:syllogism|syllogism]] based on the [[logic:inferences:modus_celarent:index|Modus Celarent]], in which a negative [[logic:glossary:existential_quantification|existential]] proposition is inferred from positive and negative universal premisses. | 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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| <html><aside><figure><h3>Modus Cesaro</h3></html>{{modus_cesaro.svg?nolink|Modus Cesaro}}<html><figcaption><a href="/app/syllogism-finder/index_en.html#EA2O">Type <code>EAO</code>, Figure <code>2</code></a><br /></html>Parent: [[logic:inferences:modus_celarent:index|Celarent]]<html></figcaption></figure></aside></html> | <html><aside><figure><h3>Modus Cesaro</h3></html>{{modus_cesaro.svg?nolink|Modus Cesaro}}<html><figcaption><a href="/app/syllogism-finder/index_en.html#EA2O">Type <code>EAO</code>, Figure <code>2</code></a><br /></html>Parent: [[logic:inferences:modus_celarent:index|Celarent]]<html></figcaption></figure></aside></html> |
| <tr><td><span title="Therefore">∴</span> Some <i>squares</i> are not <i>circles</i>.</td></tr></tbody></table></html> | <tr><td><span title="Therefore">∴</span> Some <i>squares</i> are not <i>circles</i>.</td></tr></tbody></table></html> |
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| <html><p class="info-box"></html>* **Note:** When an //existential// conclusion is inferred from //universal// premisses, this requires an (implicit or explicit) [[logic: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// (<html><abbr title="minor term">S</abbr></html>), as this also implies existence of <html><abbr title="middle term">M</abbr>, while the conclusion does not require existence for <abbr title="major term">P</abbr>.</p></html> | <html><p class="info-box"></html>* **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// (<html><abbr title="minor term">S</abbr></html>), as this also implies existence of <html><abbr title="middle term">M</abbr>, while the conclusion does not require existence for <abbr title="major term">P</abbr>.</p></html> |
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| //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//. | //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 ===== | ===== Name ===== |
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| 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 [[logic:glossary:existential_quantification|existential]] statement. | 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. |
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| ===== See also ===== | ===== See also ===== |
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| * [[logic:glossary:existential_import|Existential import]] | * [[glossary:existential_import|Existential import]] |
| * [[logic:glossary:existential_quantification|Existential quantification]] | * [[glossary:existential_quantification|Existential quantification]] |
| * [[logic:inferences:modus_celarent:index|Modus Celarent]] | * [[logic:inferences:modus_celarent:index|Modus Celarent]] |
| * [[glossary:syllogism|Syllogism]] | * [[glossary:syllogism|Syllogism]] |
