====== Existential Fallacy ======

A [[logic:formal_fallacies:index|formal fallacy]] by which //existence// is implied in a logical operation that would require it to be proven first.

Take, for example, the following [[glossary:syllogism|syllogism]]:

> All <i>animals</i> are <i>mortal</i>.   (true)
> No <i>unicorn</i> is <i>mortal</i>.   ([[glossary:vacuous_truth|vacuously true]])
> <span conclusio><s invalid "Existential fallacy">Therefore, there exists //unicorns// which are not //animals//.</s>   </span>   (//existential fallacy//)

On first glance, this resembles the [[logic:inferences:modus_celarent:modus_camestros|Modus Camestros]] [[app>#camestros|Show “Modus Camestros” in Syllogism FInder App]], but it lacks the ex­pli­cit [[glossary:existential_import|existential import]] that this form nor­mally re­quires. As a result, the //con­clu­sion// here, which implies existence of //unicorns// is not valid.

<aside info filled rounded>
**Note:** The formulation starting with “there exists …” is one of many ways that an [[glossary:existential_quantification|existential quantification]] can be transferred into natural language. This specific formulation has been chosen in this situation because it makes the existential implication obvious. This does however not mean that other formulations (e.g. “some A are B”) do not also imply existence.
</aside>

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

  * (Illicit) existential instantiation

===== Description =====

Different types of logical state­ments may or may not refer to //empty ex­ten­sions// of the terms used. Most not­ably, [[glossary:universal_quantification|uni­versal quan­ti­fi­ca­tions]] (like <q>all A are B</q>) do //not//, wheras [[glossary:existential_quantification|exis­tential quan­ti­fi­ca­tions]] (like <q>some A are B</q>) //do// imply ex­istence.

This can lead to problems when the lat­ter type is in­fered from earlier. A typ­ical situ­ation where this happens is when an //ex­is­tent­ial quan­ti­fi­ca­tion// is in­fer­red from a //uni­ver­sal// one. In prin­ci­ple, this is pos­sible, as the //exis­ten­tial quan­ti­fier// is the //weaker// form of the two (<b maniculus><i :la>[[glossary:argumentum_a_fortiori:index|Argu­mentum a Forti­ori]]</i> </b>), mean­ing that a state­ment like <q>//all// cars are vehicles</q> ob­vi­ously also im­plies that <q>//some// cars are vehicles</q>.

What is less obvious, though, is that this inference is only possible because we //know// that cars actually exist. In other words, by our knowledge (which is external to the logical statements), we implicitly [[glossary:existential_import|import existence]] into this trans­formation.

This becomes a problem with state­ments which refer to some­thing that does //not// exist: “all //uni­corns// are im­mortal” is //[[glossary:vacuous_truth|vacu­ously true]]//, mean­ing it is //true// spe­ci­fi­cally be­cause no uni­corns exist that could ac­tu­ally ever die. If we trans­form this into <q>there exist uni­corns which are im­mortal</q>, this //im­pli­cit// [[glossary:existential_import|exis­ten­tial import]] goes wrong and we have ar­rived to a state­ment which is clearly //not true//.

For this reason, infering from a form that allows re­fer­ring to an empty ex­tens­ion to one that does //not//, re­quires that the im­port is made //ex­plicit//.

Such situ­ations arise in a number of [[glossary:syllogism|syllogisms]], where an //ex­is­ten­tial// con­clu­sion is de­rived from uni­ver­sal pre­mises. In par­ti­cu­lar, this af­fects the 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 all of these, there is an ad­di­tional re­quire­ment to ex­pli­citly vali­date the //exis­ten­tial im­port// for at least one of the terms used.

However, this fallacy is not limited to syl­log­istic in­fer­ences, but can hap­pen when­ever a state­ment which has an ex­is­ten­tial im­pli­cation is de­rived from a state­ment that does not.

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

  * [[glossary:existential_import|Existential import]]
  * [[glossary:existential_quantification|Existential quantifications]]
  * [[glossary:extension|Extension]]
  * [[glossary:universal_quantification|Universal quantifications]]

===== More information =====

  * [[http://www.fallacyfiles.org/existent.html|The Existential Fallacy]] on //Fallacy Files//