Abstract Inferentialist accounts of meaning which take the primary unit of meaning to be the sentence have to answer the puzzle of subsentential structure. That is, they have to explain the ubiquity and meaning of subsentential vocabulary on inferentialist grounds. One solution to the puzzle is developed in Brandom's magnum opus Making It Explicit in the form of his argument for the existence of singular terms. However, there is earlier work devoted to similar issues: Carnap, in chapter IV of his Logical Syntax, engages in a similar project, namely in a demarcation between different kinds of subsentential structure on an inferentialist basis. In this talk, I will present and compare Carnap's and Brandom's approaches to the puzzle of subsentential structure, with an eye towards common problems and solutions to these. I will also explain how their work can be placed in the context of algebraic logic, connecting their approaches with the so-called substitution algebras studied in parts of algebraic logic.