First-order quantifiers generalize into the position occupied by a singular term or proper name, while the more controversial second-order quantifiers generalize into the position occupied by a predicate. Consider, for example, the claim that Socrates is mortal, symbolized as Ms. While first-order logic allows us to infer that there is someone who is mortal, ∃x Mx, second-order logic allows us to infer that there is some “concept” (as Frege put it) under which Socrates falls, ∃F Fs.3
