====== Existential Import ======

When a form of logical statement that implies //existence// is derived from premisses in which existence is not necessarily implied, existence must first be proven.

For example:

> All //giant squids// are deep-sea animals.
> [and //giant squids// exist.]
> There exist //giant squids// that are deep-sea animals.

“[[wp>Giant squid|Giant squid]]” refers to several species of in­verte­brates that were long thought to be merely [[wp>Sailors' superstitions|sail­or’s yarn]], i.e. some kind of mythical sea-monsters. Their ex­ist­ence has only been proven during the 20<sup>th</sup> century.

This proof of existence is re­quired in order to be able to derive an //exis­tent­ial// state­ment (which does require ex­ist­ence) from a uni­versal one (which does not re­quire it).

===== Other names =====

  * <i :de>[[de>logik/begriffe/existenzeinfuehrung|Existenzeinführung]]</i>

===== Description =====

A recurring issue in the validity of logical statements concerns the question of //existence// of the objects that the terms actually refer to. There are certain statements that are valid even if (or even //because//) they refer to an empty [[glossary:extension|extension]] of a term.

For example, all [[glossary:universal_quantification|universal statements]] (like “//all// A //are// B”) are valid even if the //extension// of their [[glossary:antecedent|antecedents]] might be empty. In fact, if we //know// that it is empty, it is even guaranteed to be true (<span maniculus "see:">[[glossary:vacuous_truth|vacuous truth]]</span>). On the other side, [[glossary:existential_quantification|existential statements]] (e.g. “//some// A //are// B”) require that the terms refer to something that actually //exists// (hence the name).

For this reason, the [[glossary:syllogism|syllogism]] forms in which an //existential// conclusion is derived from one or multiple //universal// premisses require that the existence of certain terms is proven in order to be valid. This affects the syllogistic modi  [[logic:inferences:modus_barbara:modus_barbari|Barbari]], [[logic:inferences:modus_barbara:modus_bamalip|Bamalip]], [[logic:inferences:modus_celarent:modus_calemos|Calemos]], [[logic:inferences:modus_celarent:modus_camestros|Camestros]], 
[[logic:inferences:modus_celarent:modus_celaront|Celaront]], [[logic:inferences:modus_celarent:modus_cesaro|Cesaro]],
[[logic:inferences:modus_darii:modus_darapti|Darapti]], [[logic:inferences:modus_ferio:modus_felapton|Felapton]] and [[logic:inferences:modus_ferio:modus_fesapo|Fesapo]].

In the example above, the //existential import// is made explicit by inserting a new premise. In other situation, this may be done implicitly (<span maniculus "see:">[[glossary:enthymeme|enthymeme]]</span>). Generally, it is to be preferred to do this explicitly, however, as this can help to avoid the so-called “[[logic:formal_fallacies:existential|existential fallacy]]”.

===== See also =====

  * [[glossary:enthymeme|Enthymeme]]
  * [[logic:formal_fallacies:existential|Existential fallacy]]
  * [[glossary:existential_quantification|Existential quantification]]
  * [[glossary:universal_quantification|Universal quantification]]

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