AAP 2026 CONFERENCE

Over the last ten years, there has been a turn in metaphysics and logic towards higher-order languages: languages containing higher-order quantifier expressions that quantify into non-subject positions, such as those of predicates and sentences. As Theodore Sider has recently observed, this higher-order turn promises a paradigm shift involving “elegant and more accurate modes of expression, new solutions to old problems, transformation of problem spaces, and generation of new questions”. In order to avoid the charge of obscurity, however, proponents of this higher-order turn face the challenge of explaining what their higher-order quantifier expressions mean. Andrew Bacon has recently attempted to meet this challenge by appealing to the inferential roles these quantifier expressions are intended to have. In this talk, I will argue that this attempt fails.