| Both sides previous revisionPrevious revisionNext revision | Previous revision |
| logic:inferences:modus_darii:modus_darapti [25.05.22, 21:59:19] – ↷ Links adapted because of a move operation admin | logic:inferences:modus_darii:modus_darapti [27.03.23, 22:50:09] (current) – external edit 127.0.0.1 |
|---|
| Hello all, | |
| ====== Modus Darapti ====== | ====== Modus Darapti ====== |
| |
| Form of a [[glossary:syllogism|syllogism]] based on the [[logic:inferences:modus_darii:index|Modus Darii]], in which an affirmative [[logic:glossary:existential_quantification|existential]] proposition is inferred from two affirmative [[glossary:universal_quantification|universal]] premisses. This form has an additional existential requirement. | Form of a [[glossary:syllogism|syllogism]] based on the [[logic:inferences:modus_darii:index|Modus Darii]], in which an affirmative [[glossary:existential_quantification|existential]] proposition is inferred from two affirmative [[glossary:universal_quantification|universal]] premisses. This form has an additional existential requirement. |
| |
| <html><aside><figure><h3>Modus Darapti</h3></html>{{modus_darapti.svg?nolink|Modus Darapti}}<html><figcaption><a href="/app/syllogism-finder/index_en.html#AA3I">Typ <code>AAI</code>, Form <code>3</code></a><br /></html>Parent: [[logic:inferences:modus_darii:index|Darii]]<html></figcaption></figure></aside></html> | <aside float-right> |
| > <html><table class="layout"><tbody><tr><td>All <abbr title="middle term">M</abbr> are <abbr title="major term">P</abbr>.</td></tr> | <figure> |
| | <h3>Modus Darapti</h3> |
| | {{modus_darapti.svg?nolink|Modus Darapti}} |
| | <figcaption>Typ ''AAI'', Form ''3''<span noprint> [[app>#AA3I|Modus Darapti]]</span> \\ Parent: [[logic:inferences:modus_darii:index|Darii]]</figcaption> |
| | </figure> |
| | </aside> |
| |
| <tr><td>All <abbr title="middle term">M</abbr> are <abbr title="minor term">S</abbr>.</td></tr> | > All <abbr title="middle term">M</abbr> are <abbr title="major term">P</abbr>. |
| <tr><td>[<i>and there exists at least one</i> <abbr title="middle term">M</abbr>]*</td></tr> | > All <abbr title="middle term">M</abbr> are <abbr title="minor term">S</abbr>. |
| <tr><td><hr /></td></tr> | > [<i>and there exists at least one</i> <abbr title="middle term">M</abbr>]* |
| <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> | > <span conclusio>Therefore, Some <abbr title="minor term">S</abbr> are <abbr title="major term">P</abbr>.</span> |
| |
| For example: | For example: |
| |
| > <html><table class="layout"><tbody><tr><td>All <i>squares</i> are <i>rectangles</i>.</td></tr> | > All <var>squares</var> are <var>rectangles</var>. |
| <tr><td>All <i>squares</i> are <i>polygons</i>.</td></tr> | > All <var>squares</var> are <var>polygons</var>. |
| <tr><td>[and there exists at least one <i>square</i>]*</td></tr> | > [and there exists at least one <var>square</var>]* |
| <tr><td><hr /></td></tr> | > Therefore, Some <var>polygons</var> are <var>rectangles</var>.</span> |
| <tr><td><span title="Therefore">∴</span> Some <i>polygons</i> are <i>rectangles</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) [[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 Darapti// it is sufficient to prove existence for the //middle term// (<html><abbr title="middle term">M</abbr></html>), as this also implies existence of both <html><abbr title="minor term">S</abbr> and <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 Darapti// it is sufficient to prove existence for the //middle term// (<abbr title="middle term">M</abbr>), as this also implies existence of both <abbr title="minor term">S</abbr> and <abbr title="major term">P</abbr>. |
| | </aside> |
| |
| //Modus Disamis// is very similar to the modi [[logic:inferences:modus_darii:modus_datisi|Datisi]] and [[logic:inferences:modus_darii:modus_disamis|Disamis]], except that it is based on two //universal// statements in the premisses, rather than a //universal// and an //existential// statement each. | //Modus Disamis// is very similar to the modi [[logic:inferences:modus_darii:modus_datisi|Datisi]] and [[logic:inferences:modus_darii:modus_disamis|Disamis]], except that it is based on two //universal// statements in the premisses, rather than a //universal// and an //existential// statement each. |
| ===== Name ===== | ===== Name ===== |
| |
| The name "Darapti" is a [[wp>Mnemonic|mnemonic]] term that helps to remember the most important characteristics of this mode: The "D" at the beginning indicates that it is related to the [[logic:inferences:modus_darii:index|Modus Darii]], the two "a" and the "i" indicate that affirmative [[glossary:universal_quantification|universal]] and [[logic:glossary:existential_quantification|existential]] statements make up this form. | The name "Darapti" is a [[wp>Mnemonic|mnemonic]] term that helps to remember the most important characteristics of this mode: The "D" at the beginning indicates that it is related to the [[logic:inferences:modus_darii:index|Modus Darii]], the two "a" and the "i" indicate that affirmative [[glossary:universal_quantification|universal]] and [[glossary:existential_quantification|existential]] statements make up this form. |
| |
| ===== See also ===== | ===== See also ===== |
| |
| * [[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_darii:index|Modus Darii]] | * [[logic:inferences:modus_darii:index|Modus Darii]] |
| * [[glossary:syllogism|Syllogism]] | * [[glossary:syllogism|Syllogism]] |
