Frege’s Many Existence Concepts

Gottlob Frege is usually taken to be a pioneer of the second-order theory of existence. According to this theory, existence is not a first-order concept, but is entirely captured by the existential quantifier of first-order logic. In this article, I argue against this naive interpretation of Frege’s work. In fact, Frege believed that the German verb ‘existieren’ expresses a first-order concept under which every object falls. I discuss the consequences of this fact for the interpretation of his rejection of the ontological argument. Central to my argument is a detailed analysis of Frege’s arguments concerning existence in his posthumously published dialogue with Bernhard Pünjer.