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| The principle "<i :la>[[logic:glossary:dictum_de_omni_et_nullo|dictum de omni et nullo]]</i>" (Lat.: "the maxim of all and none") states that what holds true in a (positive or negative) universal quantification is also true for every single element that the statement [[glossary:extension|extends]] to. | The principle "<i :la>[[logic:glossary:dictum_de_omni_et_nullo|dictum de omni et nullo]]</i>" (Lat.: "the maxim of all and none") states that what holds true in a (positive or negative) universal quantification is also true for every single element that the statement [[glossary:extension|extends]] to. |
| Obviously, a statement like "all horses are mammals" also implies that every single horse is a mammal, as likewise "no pig can fly" extends to every single pig (<span maniculus "see:"></span>[[glossary:distribution|distributivity]]). However, there are specific situations where this transfer does not apply. | Obviously, a statement like "all horses are mammals" also implies that every single horse is a mammal, as likewise "no pig can fly" extends to every single pig (<span maniculus "see:"></span>[[glossary:distribution|distribution]]). However, there are specific situations where this transfer does not apply. |
| * There are certain properties of groups that only [[glossary:emergence|emerge]] through the composition of the group or the interaction of the group members themselves. For example, a statement like "all the horses in this herd are differently coloured" only makes sense if the herd comprises more than one horse (<span maniculus "see:">[[logic:emergence:index|fallacies of emergence]]</span>). | * There are certain properties of groups that only [[glossary:emergence|emerge]] through the composition of the group or the interaction of the group members themselves. For example, a statement like "all the horses in this herd are differently coloured" only makes sense if the herd comprises more than one horse (<span maniculus "see:">[[logic:emergence:index|fallacies of emergence]]</span>). |
