A first-order quantifier $\exists x$ (also represented by $\Sigma x$ due to a similarity to a summation) corresponding to the phrase ‘there exists an $x$ such that…’. In a first-order model, an existentially quantified sentence $\exists x\phi \left(x\right)$ is true when there exists an element of the domain of quantification of which $\phi \left(x\right)$ is true, i.e., there exists an individual that the propositional function corresponding to $\phi \left(x\right)$ maps to a designated value. These truth conditions underscore the duality between the existential quantifier and the universal quantifier $\forall x$, which can be expressed in first-order classical logic (and in many non-classical logics) as the logical equivalence of the formulae $\exists x\phi \left(x\right)$ and $\neg \forall x\neg \phi \left(x\right)$. Although $\exists x$ is often read as ‘some $x$…’, some philosophers have held that ‘some $x$…’ does not entail that the $x$ in question exists (e.g., I am thinking of something: Father Christmas). According to this position, the existential quantifier is contrasted with the particular quantifier.