Existential Quantification Operation

AKA: ∃, Existential Quantifier, Existential Quantification, ThereExists.
Context:
- It is a Logical Quantifier.
- …
Example(s):
- [math]\displaystyle{ X \land Y \Rightarrow \exist x \in X, X \land Y }[/math].
- …
Counter-Example(s):
- a Universal Quantification Operation, such as [math]\displaystyle{ X \land Y \Rightarrow \forall x \in X, X \land Y }[/math].
See: Generalised Cartesian Product, Predicate Logic.

References

(Wikipedia, 2013) ⇒ http://en.wikipedia.org/wiki/Existential_quantification
- In predicate logic, an existential quantification is a type of quantifier, a logical constant which is interpreted as "there exists," "there is at least one," or "for some." It expresses that a propositional function can be satisfied by at least one member of a domain of discourse. In other terms, it is the predication of a property or relation to at least one member of the domain. It asserts that a predicate within the scope of an existential quantifier is true of at least one value of a predicate variable.
  It is usually denoted by the turned E (∃) logical operator symbol, which, when used together with a predicate variable, is called an existential quantifier ("∃x" or "∃(x)"). Existential quantification is distinct from universal quantification ("for all"), which asserts that the property or relation holds for all members of the domain.
  Symbols are encoded Template:Unichar and Template:Unichar.

(WordNet, 2009) ⇒ http://wordnetweb.princeton.edu/perl/webwn?s=existential%20quantifier
- S: (n) existential quantifier**, existential operator (a logical quantifier of a proposition that asserts the existence of at least one thing for which the proposition is true)

http://en.wiktionary.org/wiki/existential_quantifier
- 1. (logic) The operator, represented by the symbol ∃, used in predicate calculus to indicate that a predicate is true for at least one member of a specified set.
  - Some verbal equivalents are "there exists" or "there is".

(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 [math]\displaystyle{ n }[/math], 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 [math]\displaystyle{ n }[/math] 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.