 By “second-order logic” we understand a logic that extends ordinary first-order logic by allowing for quantification into predicate position. For instance, from “\(a\) is an apple” we can in second-order logic infer “\(\Exists{F}\mstop Fa\)”. But the plural logics described above extend ordinary first-order logic in a different way, namely by allowing quantification into plural argument position. But predicates and plural noun phrases belong to different syntactic and semantic categories. For instance, the former consists of expressions that are unsaturated (in Frege’s sense) — that is, that contain gaps or argument places — whereas the latter consists of expressions that are saturated (Higginbotham 1998: sect. 7; Oliver and Smiley 2001 and 2016; Rayo and Yablo 2001: sect. X; Simons 1997; Williamson 2003: sect. IX; Yi 2005; Florio and Linnebo 2021). Accordingly, second-order quantification and plural quantification are generally regarded as different forms of quantification. In this section I discuss some of the differences and similarities. 