On the connection between semantic content and the objects of assertion

The Rigidity Thesis states that no rigid term can have the same semantic content as a nonrigid one. Drawing on Dummett (1973; 1991), Evans (1979; 1982), and Lewis (1980), Stanley (1997a; 1997b; 2002) rejects the thesis since it relies on an illicit identification of compositional semantic content and the content of assertion (henceforth, assertoric content). I argue that Stanley's critique of the Rigidity Thesis fails since it places constraints on assertoric content that cannot be satisfied by any plausible notion of content appropriately related to compositional semantic content. For similar reasons, I also challenge a recent two-dimensionalist defense of Stanley by Ninan (2012). The moral is far-reaching: Any theory that invokes a distinction between semantic and assertoric contents is unsatisfactory unless it can plausibly explain the connection between them.