# Existential Quantification Operation

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An Existential Quantification Operation is a Predicate Logic Operation that requires a Predicate Sentence to be True for at least one Variable Member of a Logic Variable.

## References

### 2008

• (Bach, 2008) ⇒ Kent Bach. (2008). “On Referring and Not Referring.” In: Reference: Interdisciplinary Perspectives." Jeanette K. Gundel and Nancy Hedberg, editors. Oxford University Press.
• QUOTE: Like it or not, proper names do have non-referential uses, including attribute uses and predicative uses.

Consider that in standard first-order logic the role of proper names is play by individual constants and existence is represented by the existential qualifier. … We have to resort to using a formula like '∃x(x=n)', which is to say there exists something identical to n. And, when there is not such thing as $\displaystyle{ n }$, we can't use the negation of a formula of that form '¬ ∃x(x=n)', to express the truth that there isn't anything to which $\displaystyle{ n }$ is identical, because standard first-order logic disallows empty names.... Russell had a logical motivation for insisting that a genuine name be one which is (epistemically) guaranteed to have a referent.

Even more problematic is the case of negative existentials, and the related problem of empty names. (To assert, for example, that Hamlet does not exist is surely not to assert of Hamlet that he does not exist, mush less to presuppose that he exists. It is possible to argue that Hamlet is a fictional character, specifically an abstract entity created by Shakespeare.