| Both sides previous revisionPrevious revision | |
| logic:inferences:modus_celarent:modus_cesaro [27.05.22, 10:56:04] – ↷ Links adapted because of a move operation 154.54.249.205 | logic:inferences:modus_celarent:modus_cesaro [28.03.23, 18:17:39] (current) – external edit 127.0.0.1 |
|---|
| 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. | 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. |
| |
| <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> | <aside float-right> |
| | <figure> |
| | <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> |
| | </figure> |
| | </aside> |
| |
| > <html><table class="layout"><tbody><tr><td>No <abbr title="major term">P</abbr> is <abbr title="middle term">M</abbr>.</td></tr> | > No <abbr "major term">P</abbr> is <abbr "middle term">M</abbr>. |
| <tr><td>All <abbr title="minor term">S</abbr> are <abbr title="middle term">M</abbr>.</td></tr> | > All <abbr "minor term">S</abbr> are <abbr "middle term">M</abbr>. |
| <tr><td>[<i>and there exists at least one</i> <abbr title="minor term">S</abbr>]*</td></tr> | > [<i>and there exists at least one</i> <abbr "minor term">S</abbr>]* |
| <tr><td><hr /></td></tr> | > <span conclusio>Therefore, Some <abbr "minor term">S</abbr> are not <abbr "major term">P</abbr>.</span> |
| <tr><td><span title="Therefore">∴</span> Some <abbr title="minor term">S</abbr> are not <abbr title="major term">P</abbr>.</td></tr></tbody></table></html> | |
| |
| For example: | For example: |
| |
| > <html><table class="layout"><tbody><tr><td>No <i>circle</i> is a <i>rectangle</i>.</td></tr> | > No <i>circle</i> is a <i>rectangle</i>. |
| <tr><td>All <i>squares</i> are <i>rectangles</i>.</td></tr> | > All <i>squares</i> are <i>rectangles</i>. |
| <tr><td>[and there exists at least one <i>square</i>]*</td></tr> | > [and there exists at least one <i>square</i>]* |
| <tr><td><hr /></td></tr> | > <span conclusio>Therefore, Some <i>squares</i> are not <i>circles</i>.</span> |
| <tr><td><span title="Therefore">∴</span> Some <i>squares</i> are not <i>circles</i>.</td></tr></tbody></table></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> | <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 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//. | //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//. |
