exists

Exists is the third-person singular present tense of the verb to exist. It denotes that something has actual being or reality, as opposed to being fictional or nonexistent. In ordinary language, exists is used to assert the presence or reality of a thing, concept, or phenomenon. The term is frequently used with there in existential constructions: There exists a solution to the problem.

In formal logic and mathematics, existence is formalized with the existential quantifier, symbolized as there exists or ∃. A statement such as There exists an x such that P(x) asserts that at least one object satisfies P. Existence statements are contrasted with universal statements (for all). Existence can be constructive (providing a witness) or non-constructive (guaranteed by theory without presenting a witness).

In philosophy, existence is central to ontology and metaphysics, addressing what objects count as being and how they relate to categories such as abstract versus concrete entities. The phrase existence precedes essence is associated with existentialist thought, though discussions of existence span many philosophical traditions. The question of what exists, and in what sense, intersects with debates about mind, language, science, and reality, and it remains a foundational issue in analytic and continental philosophy alike.