 Both Frege and Russell combine their account of quantification in terms of predication with the substantive thesis that existence is to be understood in terms of quantification. For Frege, existence is to be identified with the second-level concept expressed by the second-level predicate expressed by \(\exists\). For Russell, existence is identified with a certain property of propositional functions, e.g., being sometimes true. This may seem overkill; if true, it might seem that only first-level concepts exist, not the objects they instantiate. For only first-level concepts are instances of the second-level concept expressed by  \(\exists\).[17]  Instead, they are mostly concerned with the thesis that statements of existence such as (7) are not cases in which a primitive property of existence is predicated of an object, but rather should be understood as an implicitly quantified statement such as (8), which is to be analyzed in terms of predication in (9) and (10) for Frege and Russell, respectively: