# Definition of existential quantifier in English:

## existential quantifier

### noun

Logic
• A formal expression used in asserting that something exists of which a stated general proposition can be said to be true.

• ‘By contraposition and the definition of the existential quantifier, the latter axiom is equivalent to x = x y (y = x).’
• ‘The epsilon calculus is, in its most basic form, an extension of first-order predicate logic with an ‘epsilon operation’ that picks out, for any true existential formula, a witness to the existential quantifier.’
• ‘In each case, the proposition expressed is argued to be that which would be expressed if the indefinite determiner were replaced by the existential quantifier.’
• ‘On this view, existence is no longer seen as a (first-level) predicate, but instead, existential statements are analyzed in terms of the (second-level) predicate is instantiated, represented by the existential quantifier.’
• ‘Disjunction, implication and the existential quantifier are definable making free use of double negation.’