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How did Gottlob Frege explain the statement that horses exist?

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Marble bust of Aristotle with a beard and draped robe, showing detailed facial features and wavy hair, set against a dark background. — metaphysics Detail of a Roman copy (2nd century bce) of a Greek alabaster portrait bust of Aristotle (c. 325 bce); in the collection of the Museo Nazionale Romano, Rome.

In the context of metaphysics, Gottlob Frege challenged the traditional view that existence is a property or attribute of an object. While some philosophers argued that existence functions as a predicate—similar to how "biting" describes a tiger—Frege maintained that such statements are only apparently about their grammatical subjects.123

Instead, Frege explained the statement "Horses exist" by reinterpreting it through the lens of symbolic logic. He argued that the statement actually means: "The number of objects that fall under the concept horse is not zero." By treating existence as a higher-order function rather than a property of individual things, Frege provided a framework that helped demonstrate why certain traditional arguments, such as the ontological argument for the existence of God, are logically unsound.132