Existences

Existences refer to the state of being real or actual across different domains. In ordinary language they distinguish what has objective reality from what is imagined or hypothetical. In philosophy existences are analyzed apart from properties or essences. In logic, existence is expressed by existential quantification: “there exists x such that P(x)” asserts that some object with property P exists within the domain of discourse.

In ontology, existences are contrasted with essence and with classification within categories of being. Philosophers distinguish contingent existences, things that could have not existed, from necessary existences, things that must exist in every possible world. Debates address whether ordinary objects exist independently of thought, and whether existence can be predicated of predicates or concepts as such.

Historically, discussions of existences run from Aristotle’s analysis of beings and causes to medieval discussions of esse and God, through modern debates in metaphysics and epistemology. The analytic tradition emphasizes a linguistic and logical treatment: existences are not simple properties of objects but features of how we quantify over them. Frege and Russell linked existence to quantification rather than predication; some philosophers, such as Meinong, argued that nonexistent existences can be objects of thought, while others deny legitimate predication of existence to such existences.

In mathematics, existences are demonstrated through proofs within formal systems. Constructive proofs provide explicit examples, while non-constructive proofs establish existences without construction. The status of mathematical existences depends on the adopted axioms and the foundational framework.

Outside philosophy and mathematics, discussions of existences appear in science, linguistics, and literature, where fictional, hypothetical, or potential existences are analyzed. The concept thus relates to truth conditions, reference, and the limits of knowledge.