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| logic:inferences:modus_barbara:modus_barbari [27.05.22, 00:21:30] – ↷ Links adapted because of a move operation 185.185.217.76 | logic:inferences:modus_barbara:modus_barbari [27.03.23, 18:32:19] (current) – admin |
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| A weaker form of the [[logic:inferences:modus_barbara:index|Modus Barbara]], in which only an existential conclusion is inferred. This form has an additional existential requirement. | A weaker form of the [[logic:inferences:modus_barbara:index|Modus Barbara]], in which only an existential conclusion is inferred. This form has an additional existential requirement. |
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| <html><aside><figure><h3>Modus Barbari</h3></html>{{modus_barbari.svg?nolink|Modus Barbari}}<html><figcaption><a href="/app/syllogism-finder/index_en.html#AA1I">Type <code>AAI</code>, Figure <code>1</code></a><br /></html>Parent: [[logic:inferences:modus_barbara:index|Barbara]]<html></figcaption></figure></aside></html> | <aside float-right> |
| | <figure> |
| | <h3>Modus Barbari</h3> |
| | {{modus_barbari.svg?nolink|Modus Barbari}} |
| | <figcaption>Type ''AAI'', Figure ''1''<span noprint> [[app>#AA1I|Modus Barbari]]</span> \\ Parent: [[logic:inferences:modus_barbara:index|Barbara]]</figcaption> |
| | </figure> |
| | </aside> |
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| > <html><table class="layout"><tbody><tr><td>All <abbr title="middle term">M</abbr> are <abbr title="major term">P</abbr>.</td></tr> | > All <abbr "middle term">M</abbr> are <abbr "major term">P</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 <abbr "major term">P</abbr>.</span> |
| <tr><td><span title="Therefore">∴</span> Some <abbr title="minor term">S</abbr> are <abbr title="major term">P</abbr>.</td></tr></tbody></table></html> | |
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| For example: | For example: |
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| > <html><table class="layout"><tbody><tr><td>All <em>rectangles</em> are <em>polygons</em>.</td></tr> | > All <var>rectangles</var> are <var>polygons</var>. |
| <tr><td>All <em>squares</em> are <em>rectangles</em>.</td></tr> | > All <var>squares</var> are <var>rectangles</var>. |
| <tr><td>[and there exists at least one <i>square</abbr> </i>]*</td></tr> | > [<i>and there exists at least one</i> square]* |
| <tr><td><hr /></td></tr> | > <span conclusio>Therefore, some <em>squares</em> are <em>polygons</em>.</span> |
| <tr><td><span title="Therefore">∴</span> Some <em>squares</em> are <em>polygons</em>.</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) [[glossary:existential_import|existential import]], i.e. it must be proven that what the term refers to actually //exists//. In case of the //Modus Barbari// it is sufficient to prove the existence of the //minor term// (<html><abbr title="minor term">S</abbr></html>), as this also implies the existence of <html><abbr title="middle term">M</abbr> and <abbr title="major term">P</abbr>.</p></html> | <aside info-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 Barbari// it is sufficient to prove the existence of the //minor term// (<abbr "minor term">S</abbr>), as this also implies the existence of <abbr "middle term">M</abbr> and <abbr "major term">P</abbr>. |
| | </aside> |
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| The //Modus Bamalip// is a weaker form of the [[logic:inferences:modus_barbara:index|Modus Barbara]], in which the conclusion is an [[glossary:existential_quantification|existential]] rather than a universal statement. 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 Barbara//. | The //Modus Bamalip// is a weaker form of the [[logic:inferences:modus_barbara:index|Modus Barbara]], in which the conclusion is an [[glossary:existential_quantification|existential]] rather than a universal statement. 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 Barbara//. |
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| Moreover, this form resembles the [[logic:inferences:modus_barbara:modus_bamalip|Modus Bamalip]], except that //middle term// (<html><abbr title="middle term">M</abbr></html>) appears in the other positions in the premises. | Moreover, this form resembles the [[logic:inferences:modus_barbara:modus_bamalip|Modus Bamalip]], except that //middle term// (<abbr "middle term">M</abbr>) appears in the other positions in the premises. |
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| ===== Name ===== | ===== Name ===== |
