How did the logical treatment of existence challenge the ontological argument for God’s existence?

The ontological argument for God’s existence, famously formulated by St. Anselm and later René Descartes, relies on the assumption that existence is a perfection or an attribute that can be predicated of a subject. By defining God as an unsurpassably perfect being, the argument posits that God must possess the attribute of existence to be truly perfect.12

Modern logic, particularly the development of predicate logic by Gottlob Frege and others, challenged this by rejecting the idea that existence is a predicate. In modern logical systems, existence is not a property attributed to an individual; rather, it is expressed through the existential quantifier ($\exists x$). To say that something exists is to assert that a concept is instantiated—that there is at least one object that falls under that concept.234

Consequently, philosophers like Immanuel Kant and Bertrand Russell argued that existence cannot be added to a definition to guarantee reality. Whether a concept is instantiated is a question of fact that cannot be determined a priori through logical definition alone.235