1. existential quantifier.

2. A quantifier $\text{P}x$ corresponding to the expression ‘some $x$ is such that…’ for which the truth of a formula $\text{P}x\phi \left(x\right)$ does not entail the existence of an individual $a$ satisfying $\phi \left(x\right)$. Importantly, advocates of many non-classical logics insist on a distinction between the particular quantifier and the existential quantifier $\exists x$. Although $\exists x\phi \left(x\right)$ is often read as ‘some $x$ satisfies $\phi \left(x\right)$’, that $\exists x$ accurately captures the phrase ‘some $x$’ is sometimes rejected on the grounds that the meaning of a sentence employing the expression ‘some $x$’ does not include a presumption of the existence of a witnessing individual. For example, the sentence

• • Some of the offspring of Uranus and Gaia were monstrous.

is arguably true despite the fact that the offspring do not exist. Hence, some formal accounts distinguishing the existential and particular quantifiers entail that while $\exists x$ quantifies over existent individuals, $\text{P}x$ may quantify over non-existent individuals as well (such as, e.g., the non-existent objects in the ontology espoused by philosopher Alexius Meinong (1853–1920)).